Colonization to Construction: Bridging the Gap Between Ancient Chamorro, Spanish Colonial & Modern Architecture on Guam

Guam is an island in the Marianas that, over time, has experienced a rich cultural history brought about by its exposure to colonization, natural disasters, warfare and the continual influx of people and culture. Therefore, the architecture that exists on the island is one that divides itself into four distinct styles with each as a response to external forces that affected the island. By researching each of these styles, one is able to fully understand the holistic view of Guam’s history in order to design architecture that reflects the past with anticipation for the future. This thesis works to explore the four styles by understanding their strengths and shortcomings in order to use this knowledge to design a Cultural Center for Art and Architecture where each style is represented

A Landau–Kolmogorov inequality for generators of families of bounded operators

AbstractA Landau–Kolmogorov type inequality for generators of a wide class of strongly continuous families of bounded and linear operators defined on a Banach space is shown. Our approach allows us to recover (in a unified way) known results about uniformly bounded C0-semigroups and cosine functions as well as to prove new results for other families of operators. In particular, if A is the generator of an α-times integrated family of bounded and linear operators arising from the well-posedness of fractional differential equations of order β+1 then, we prove that the inequality‖Ax‖2⩽8M2Γ(α+β+2)2Γ(α+1)Γ(α+2β+3)‖x‖‖A2x‖, holds for all x∈D(A2)

Fundamental solutions for semidiscrete evolution equations via Banach algebras

We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fourier transform. We consider finite difference operators of first and second orders, which are generators of uniformly continuous semigroups and cosine functions. We present the linear and algebraic structures (in particular, factorization properties) and their norms and spectra in the Lebesgue space of summable sequences. We identify fractional powers of these generators and apply to them the subordination principle. We also give some applications and consequences of our results

Dynamics of the solutions of the water hammer equations

NOTICE: this is the author’s version of a work that was accepted for publication in Topology and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Topology and its Applications, [Volume 203, 15 April 2016, Pages 67-83] DOI10.1016/j.topol.2015.12.076¨[EN] In this note we provide a representation of the solution using an operator theoretical approach based on the theory of C-0-semigroups and cosine operator functions, when considering this phenomenon on a compressible fluid along an infinite pipe. We provide an integro-differential equation that represents this phenomenon and it only involves the discharge. In addition, the representation of the solution in terms of a specific C-0-semigroup lets us show that hypercyclicity and the topologically mixing property can occur when considering this phenomenon on certain weighted spaces of integrable and continuous functions on the real line. (C) 2016 Elsevier B.V. All rights reserved.The first and third authors are supported by MEC Projects MTM2010-14909 and MTM2013-47093-P. The first author is also supported by Programa de Investigación y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by CONICYT, under Fondecyt Grant number 1140258.Conejero, JA.; Lizama, C.; Ródenas Escribá, FDA. (2016). Dynamics of the solutions of the water hammer equations. Topology and its Applications. 203:67-83. https://doi.org/10.1016/j.topol.2015.12.076S678320

On the boundedness of generalized Ces\`aro operators on Sobolev spaces

For $\beta>0$ and $p\ge 1$, the generalized Ces\`aro operator $$\mathcal{C}_\beta f(t):=\frac{\beta}{t^\beta}\int_0^t (t-s)^{\beta-1}f(s)ds$$ and its companion operator $\mathcal{C}_\beta^*$ defined on Sobolev spaces $\mathcal{T}_p^{(\alpha)}(t^\alpha)$ and $\mathcal{T}_p^{(\alpha)}(| t|^\alpha)$ (where $\alpha\ge 0$ is the fractional order of derivation and are embedded in L^p(\RR^+) and L^p(\RR) respectively) are studied. We prove that if $p>1$, then $\mathcal{C}_\beta$ and $\mathcal{C}_\beta^*$ are bounded operators and commute on $\mathcal{T}_p^{(\alpha)}(t^\alpha)$ and $\mathcal{T}_p^{(\alpha)}(| t|^\alpha)$. We show explicitly the spectra $\sigma (\mathcal{C}_\beta)$ and $\sigma (\mathcal{C}_\beta^*)$ and its operator norms (which depend on $p$). For $1< p\le 2$, we prove that $\hat{{\mathcal C}_\beta(f)}={\mathcal C}_\beta^*(\hat{f})$ and $\hat{{\mathcal C}_\beta^*(f)}={\mathcal C}_\beta(\hat{f})$ where $\hat{f}$ is the Fourier transform of a function f\in L^p(\RR).Comment: 24 page

Quantum Flows for Secret Key Distribution

Despite the unconditionally secure theory of quantum key distribution (QKD), several attacks have been successfully implemented against commercial QKD systems. Those systems have exhibited some flaws, as the secret key rate of corresponding protocols remains unaltered, while the eavesdropper obtains the entire secret key. We propose a new theoretical approach called quantum flows to be able to detect the eavesdropping activity in the channel without requiring additional optical components different from the BB84 protocol because the system can be implemented as a high software module. In this approach, the transmitter interleaves pairs of quantum states, referred to here as parallel and orthogonal (non-orthogonal) states, while the receiver uses active basis selection

Linear dynamics of semigroups generated by differential operators

[EN] During the last years, several notions have been introduced for describing the dynamical behavior of linear operators on infinite-dimensional spaces, such as hypercyclicity, chaos in the sense of Devaney, chaos in the sense of Li-Yorke, subchaos, mixing and weakly mixing properties, and frequent hypercyclicity, among others. These notions have been extended, as far as possible, to the setting of C0-semigroups of linear and continuous operators. We will review some of these notions and we will discuss basic properties of the dynamics of C0-semigroups. We will also study in detail the dynamics of the translation C0-semigroup on weighted spaces of integrable functions and of continuous functions vanishing at infinity. Using the comparison lemma, these results can be transferred to the solution C0-semigroups of some partial differential equations. Additionally, we will also visit the chaos for infinite systems of ordinary differential equations, that can be of interest for representing birth-and-death process or car-following traffic models.The first, third and fourth authors were supported by MINECO and FEDER, grant MTM2016-75963-P. The second author has been partially supported by CONICYT under FONDECYT grant number 1140258 and CONICYT-PIA-Anillo ACT1416.Conejero, JA.; Lizama, C.; Murillo Arcila, M.; Peris Manguillot, A. (2017). Linear dynamics of semigroups generated by differential operators. Open Mathematics. 15(1):745-767. https://doi.org/10.1515/math-2017-0065S745767151Herzog, G. (1997). On a Universality of the Heat Equation. Mathematische Nachrichten, 188(1), 169-171. doi:10.1002/mana.19971880110Kalmes, T. (2010). Hypercyclicity and mixing for cosine operator functions generated by second order partial differential operators. Journal of Mathematical Analysis and Applications, 365(1), 363-375. doi:10.1016/j.jmaa.2009.10.063Bayart, F., & Grivaux, S. (2006). Frequently hypercyclic operators. Transactions of the American Mathematical Society, 358(11), 5083-5117. doi:10.1090/s0002-9947-06-04019-0Bermúdez, T., Bonilla, A., Martínez-Giménez, F., & Peris, A. (2011). Li–Yorke and distributionally chaotic operators. Journal of Mathematical Analysis and Applications, 373(1), 83-93. doi:10.1016/j.jmaa.2010.06.011Gethner, R. M., & Shapiro, J. H. (1987). Universal vectors for operators on spaces of holomorphic functions. Proceedings of the American Mathematical Society, 100(2), 281-281. doi:10.1090/s0002-9939-1987-0884467-4Kalmes, T. (2006). On chaotic $C_0$-semigroups and infinitely regular hypercyclic vectors. Proceedings of the American Mathematical Society, 134(10), 2997-3002. doi:10.1090/s0002-9939-06-08391-2Banasiak, J., & Moszyński, M. (2008). Hypercyclicity and chaoticity spaces of $C_0$ semigroups. Discrete & Continuous Dynamical Systems - A, 20(3), 577-587. doi:10.3934/dcds.2008.20.577UCHI, S. (1973). Semi-groups of operators in locally convex spaces. Journal of the Mathematical Society of Japan, 25(2), 265-276. doi:10.2969/jmsj/02520265Mangino, E. M., & Peris, A. (2011). Frequently hypercyclic semigroups. Studia Mathematica, 202(3), 227-242. doi:10.4064/sm202-3-2Conejero, J. A., Martínez-Giménez, F., Peris, A., & Ródenas, F. (2015). Chaotic asymptotic behaviour of the solutions of the Lighthill–Whitham–Richards equation. Nonlinear Dynamics, 84(1), 127-133. doi:10.1007/s11071-015-2245-4Costakis, G., & Peris, A. (2002). Hypercyclic semigroups and somewhere dense orbits. Comptes Rendus Mathematique, 335(11), 895-898. doi:10.1016/s1631-073x(02)02572-4Murillo-Arcila, M., & Peris, A. (2014). Chaotic Behaviour on Invariant Sets of Linear Operators. Integral Equations and Operator Theory, 81(4), 483-497. doi:10.1007/s00020-014-2188-zMurillo-Arcila, M., & Peris, A. (2013). Strong mixing measures for linear operators and frequent hypercyclicity. Journal of Mathematical Analysis and Applications, 398(2), 462-465. doi:10.1016/j.jmaa.2012.08.050Marchand, R., McDevitt, T., & Triggiani, R. (2012). An abstract semigroup approach to the third-order Moore-Gibson-Thompson partial differential equation arising in high-intensity ultrasound: structural decomposition, spectral analysis, exponential stability. Mathematical Methods in the Applied Sciences, 35(15), 1896-1929. doi:10.1002/mma.1576Grosse-Erdmann, K.-G. (2000). Hypercyclic and chaotic weighted shifts. Studia Mathematica, 139(1), 47-68. doi:10.4064/sm-139-1-47-68Birkhoff, G. D. (1922). Surface transformations and their dynamical applications. Acta Mathematica, 43(0), 1-119. doi:10.1007/bf02401754DESCH, W., SCHAPPACHER, W., & WEBB, G. F. (1997). Hypercyclic and chaotic semigroups of linear operators. Ergodic Theory and Dynamical Systems, 17(4), 793-819. doi:10.1017/s0143385797084976Li, T.-Y., & Yorke, J. A. (1975). Period Three Implies Chaos. The American Mathematical Monthly, 82(10), 985-992. doi:10.1080/00029890.1975.11994008Bernal-González, L. (1999). Hypercyclic Sequences of Differential and Antidifferential Operators. Journal of Approximation Theory, 96(2), 323-337. doi:10.1006/jath.1998.3237LI, K., & GAO, Z. (2004). NONLINEAR DYNAMICS ANALYSIS OF TRAFFIC TIME SERIES. Modern Physics Letters B, 18(26n27), 1395-1402. doi:10.1142/s0217984904007943Barrachina, X., & Peris, A. (2012). Distributionally chaotic translation semigroups. Journal of Difference Equations and Applications, 18(4), 751-761. doi:10.1080/10236198.2011.625945Chang, S.-J., & Chen, C.-C. (2013). Topological mixing for cosine operator functions generated by shifts. Topology and its Applications, 160(2), 382-386. doi:10.1016/j.topol.2012.11.018Salas, H. N. (1995). Hypercyclic weighted shifts. Transactions of the American Mathematical Society, 347(3), 993-1004. doi:10.1090/s0002-9947-1995-1249890-6Aron, R. M., Seoane-Sepúlveda, J. B., & Weber, A. (2005). Chaos on function spaces. Bulletin of the Australian Mathematical Society, 71(3), 411-415. doi:10.1017/s0004972700038417Desch, W., & Schappacher, W. (2008). Hypercyclicity of Semigroups is a Very Unstable Property. Mathematical Modelling of Natural Phenomena, 3(7), 148-160. doi:10.1051/mmnp:2008047Albanese, A., Barrachina, X., Mangino, E. M., & Peris, A. (2013). Distributional chaos for strongly continuous semigroups of operators. Communications on Pure and Applied Analysis, 12(5), 2069-2082. doi:10.3934/cpaa.2013.12.2069Conejero, J. A., Lizama, C., & Rodenas, F. (2016). Dynamics of the solutions of the water hammer equations. Topology and its Applications, 203, 67-83. doi:10.1016/j.topol.2015.12.076Rubinow, S. I. (1968). A Maturity-Time Representation for Cell Populations. Biophysical Journal, 8(10), 1055-1073. doi:10.1016/s0006-3495(68)86539-7Brzeźniak, Z., & Dawidowicz, A. L. (2008). On periodic solutions to the von Foerster-Lasota equation. Semigroup Forum, 78(1), 118-137. doi:10.1007/s00233-008-9120-2Frerick, L., Jordá, E., Kalmes, T., & Wengenroth, J. (2014). Strongly continuous semigroups on some Fréchet spaces. Journal of Mathematical Analysis and Applications, 412(1), 121-124. doi:10.1016/j.jmaa.2013.10.053Rudnicki, R. (2015). An ergodic theory approach to chaos. Discrete & Continuous Dynamical Systems - A, 35(2), 757-770. doi:10.3934/dcds.2015.35.757JI, L., & WEBER, A. (2009). Dynamics of the heat semigroup on symmetric spaces. Ergodic Theory and Dynamical Systems, 30(2), 457-468. doi:10.1017/s0143385709000133Ovsepian, R., & Pełczyński, A. (1975). On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bounded orthonormal systems in L². Studia Mathematica, 54(2), 149-159. doi:10.4064/sm-54-2-149-159Conejero, J. A., & Mangino, E. M. (2010). Hypercyclic Semigroups Generated by Ornstein-Uhlenbeck Operators. Mediterranean Journal of Mathematics, 7(1), 101-109. doi:10.1007/s00009-010-0030-7MARTÍNEZ-GIMÉNEZ, F., & PERIS, A. (2002). CHAOS FOR BACKWARD SHIFT OPERATORS. International Journal of Bifurcation and Chaos, 12(08), 1703-1715. doi:10.1142/s0218127402005418Banks, J., Brooks, J., Cairns, G., Davis, G., & Stacey, P. (1992). On Devaney’s Definition of Chaos. The American Mathematical Monthly, 99(4), 332-334. doi:10.1080/00029890.1992.11995856Rolewicz, S. (1969). On orbits of elements. Studia Mathematica, 32(1), 17-22. doi:10.4064/sm-32-1-17-22Bayart, F., & Grivaux, S. (2005). Hypercyclicity and unimodular point spectrum. Journal of Functional Analysis, 226(2), 281-300. doi:10.1016/j.jfa.2005.06.001Bayart, F., & Matheron, É. (2007). Hypercyclic operators failing the Hypercyclicity Criterion on classical Banach spaces. Journal of Functional Analysis, 250(2), 426-441. doi:10.1016/j.jfa.2007.05.001Peris, A., & Saldivia, L. (2005). Syndetically Hypercyclic Operators. Integral Equations and Operator Theory, 51(2), 275-281. doi:10.1007/s00020-003-1253-9Metz, J. A. J., Staňková, K., & Johansson, J. (2015). The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin’s maximum principle. Journal of Mathematical Biology, 72(4), 1125-1152. doi:10.1007/s00285-015-0938-4PROTOPOPESCU, V., & AZMY, Y. Y. (1992). TOPOLOGICAL CHAOS FOR A CLASS OF LINEAR MODELS. Mathematical Models and Methods in Applied Sciences, 02(01), 79-90. doi:10.1142/s0218202592000065Banasiak, J., & Moszyński, M. (2011). Dynamics of birth-and-death processes with proliferation - stability and chaos. Discrete & Continuous Dynamical Systems - A, 29(1), 67-79. doi:10.3934/dcds.2011.29.67A. Conejero, J., & Peris, A. (2009). Hypercyclic translation $C_0$-semigroups on complex sectors. Discrete & Continuous Dynamical Systems - A, 25(4), 1195-1208. doi:10.3934/dcds.2009.25.1195Conejero, J. A. (2007). On the Existence of Transitive and Topologically Mixing Semigroups. Bulletin of the Belgian Mathematical Society - Simon Stevin, 14(3), 463-471. doi:10.36045/bbms/1190994207Grosse-Erdmann, K.-G. (1999). Universal families and hypercyclic operators. Bulletin of the American Mathematical Society, 36(03), 345-382. doi:10.1090/s0273-0979-99-00788-0Banasiak, J., Lachowicz, M., & Moszynski, M. (2006). Semigroups for Generalized Birth-and-Death Equations in lp Spaces. Semigroup Forum, 73(2), 175-193. doi:10.1007/s00233-006-0621-xCONEJERO, J. A., PERIS, A., & TRUJILLO, M. (2010). CHAOTIC ASYMPTOTIC BEHAVIOR OF THE HYPERBOLIC HEAT TRANSFER EQUATION SOLUTIONS. International Journal of Bifurcation and Chaos, 20(09), 2943-2947. doi:10.1142/s0218127410027489Bermúdez, T., Bonilla, A., Conejero, J. A., & Peris, A. (2005). Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces. Studia Mathematica, 170(1), 57-75. doi:10.4064/sm170-1-3Aroza, J., & Peris, A. (2012). Chaotic behaviour of birth-and-death models with proliferation. Journal of Difference Equations and Applications, 18(4), 647-655. doi:10.1080/10236198.2011.631535deLaubenfels, R., Emamirad, H., & Protopopescu, V. (2000). Linear Chaos and Approximation. Journal of Approximation Theory, 105(1), 176-187. doi:10.1006/jath.2000.3465Aron, R., & Markose, D. (2004). ON UNIVERSAL FUNCTIONS. Journal of the Korean Mathematical Society, 41(1), 65-76. doi:10.4134/jkms.2004.41.1.065Chang, Y.-H., & Hong, C.-H. (2012). THE CHAOS OF THE SOLUTION SEMIGROUP FOR THE QUASI-LINEAR LASOTA EQUATION. Taiwanese Journal of Mathematics, 16(5), 1707-1717. doi:10.11650/twjm/1500406791Badea, C., & Grivaux, S. (2007). Unimodular eigenvalues, uniformly distributed sequences and linear dynamics. Advances in Mathematics, 211(2), 766-793. doi:10.1016/j.aim.2006.09.010Wijngaarden, L. V. (1972). One-Dimensional Flow of Liquids Containing Small Gas Bubbles. Annual Review of Fluid Mechanics, 4(1), 369-396. doi:10.1146/annurev.fl.04.010172.002101Dyson, J., Villella-Bressan, R., & Webb, G. (1997). Hypercyclicity of solutions of a transport equation with delays. Nonlinear Analysis: Theory, Methods & Applications, 29(12), 1343-1351. doi:10.1016/s0362-546x(96)00192-7Eringen, A. C. (1990). Theory of thermo-microstretch fluids and bubbly liquids. International Journal of Engineering Science, 28(2), 133-143. doi:10.1016/0020-7225(90)90063-oBayart, F., & Bermúdez, T. (2009). Semigroups of chaotic operators. Bulletin of the London Mathematical Society, 41(5), 823-830. doi:10.1112/blms/bdp055Bernardes, N. C., Bonilla, A., Müller, V., & Peris, A. (2013). Distributional chaos for linear operators. Journal of Functional Analysis, 265(9), 2143-2163. doi:10.1016/j.jfa.2013.06.019Webb, G. F. (1987). Random transitions, size control, and inheritance in cell population dynamics. Mathematical Biosciences, 85(1), 71-91. doi:10.1016/0025-5564(87)90100-3Bartoll, S., Martínez-Giménez, F., & Peris, A. (2016). Operators with the specification property. Journal of Mathematical Analysis and Applications, 436(1), 478-488. doi:10.1016/j.jmaa.2015.12.004Godefroy, G., & Shapiro, J. H. (1991). Operators with dense, invariant, cyclic vector manifolds. Journal of Functional Analysis, 98(2), 229-269. doi:10.1016/0022-1236(91)90078-jBAYART, F., & RUZSA, I. Z. (2013). Difference sets and frequently hypercyclic weighted shifts. Ergodic Theory and Dynamical Systems, 35(3), 691-709. doi:10.1017/etds.2013.77Bartoll, S., Martínez-Giménez, F., & Peris, A. (2012). The specification property for backward shifts. Journal of Difference Equations and Applications, 18(4), 599-605. doi:10.1080/10236198.2011.586636Li, T. (2005). Nonlinear dynamics of traffic jams. Physica D: Nonlinear Phenomena, 207(1-2), 41-51. doi:10.1016/j.physd.2005.05.011Dawidowicz, A. L., & Poskrobko, A. (2008). On chaotic and stable behaviour of the von Foerster–Lasota equation in some Orlicz spaces. Proceedings of the Estonian Academy of Sciences, 57(2), 61. doi:10.3176/proc.2008.2.01Aroza, J., Kalmes, T., & Mangino, E. (2014). ChaoticC0-semigroups induced by semiflows in Lebesgue and Sobolev spaces. Journal of Mathematical Analysis and Applications, 412(1), 77-98. doi:10.1016/j.jmaa.2013.10.002Bès, J., & Peris, A. (1999). Hereditarily Hypercyclic Operators. Journal of Functional Analysis, 167(1), 94-112. doi:10.1006/jfan.1999.3437Martínez-Giménez, F., Oprocha, P., & Peris, A. (2009). Distributional chaos for backward shifts. Journal of Mathematical Analysis and Applications, 351(2), 607-615. doi:10.1016/j.jmaa.2008.10.049Murillo-Arcila, M., Miana, P. J., Kostić, M., & Conejero, J. A. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis, 15(5), 1915-1939. doi:10.3934/cpaa.2016022Rudnicki, R. (2004). Chaos for some infinite-dimensional dynamical systems. Mathematical Methods in the Applied Sciences, 27(6), 723-738. doi:10.1002/mma.498Albanese, A. A., Bonet, J., & Ricker, W. J. (2010). C0-semigroups and mean ergodic operators in a class of Fréchet spaces. Journal of Mathematical Analysis and Applications, 365(1), 142-157. doi:10.1016/j.jmaa.2009.10.014Lasota, A., Mackey, M. C., & Ważewska-Czyżewska, M. (1981). Minimizing therapeutically induced anemia. Journal of Mathematical Biology, 13(2), 149-158. doi:10.1007/bf00275210Wu, X. (2013). Li–Yorke chaos of translation semigroups. Journal of Difference Equations and Applications, 20(1), 49-57. doi:10.1080/10236198.2013.809712Costakis, G., & Sambarino, M. (2004). Genericity of wild holomorphic functions and common hypercyclic vectors. Advances in Mathematics, 182(2), 278-306. doi:10.1016/s0001-8708(03)00079-3Schweizer, B., & Smítal, J. (1994). Measures of chaos and a spectral decomposition of dynamical systems on the interval. Transactions of the American Mathematical Society, 344(2), 737-754. doi:10.1090/s0002-9947-1994-1227094-xBanasiak, J., Lachowicz, M., & Moszyński, M. (2007). Chaotic behavior of semigroups related to the process of gene amplification–deamplification with cell proliferation. Mathematical Biosciences, 206(2), 200-215. doi:10.1016/j.mbs.2005.08.004Beauzamy, B. (1987). An operator on a separable Hilbert space with many hypercyclic vectors. Studia Mathematica, 87(1), 71-78. doi:10.4064/sm-87-1-71-78Dembart, B. (1974). On the theory of semigroups of operators on locally convex spaces. Journal of Functional Analysis, 16(2), 123-160. doi:10.1016/0022-1236(74)90061-5Muñoz-Fernández, G. A., Seoane-Sepúlveda, J. B., & Weber, A. (2011). Periods of strongly continuous semigroups. Bulletin of the London Mathematical Society, 44(3), 480-488. doi:10.1112/blms/bdr109KALMES, T. (2007). Hypercyclic, mixing, and chaotic C0-semigroups induced by semiflows. Ergodic Theory and Dynamical Systems, 27(5), 1599-1631. doi:10.1017/s0143385707000144Bès, J., Menet, Q., Peris, A., & Puig, Y. (2015). Recurrence properties of hypercyclic operators. Mathematische Annalen, 366(1-2), 545-572. doi:10.1007/s00208-015-1336-3Read, C. J. (1988). The invariant subspace problem for a class of Banach spaces, 2: Hypercyclic operators. Israel Journal of Mathematics, 63(1), 1-40. doi:10.1007/bf02765019BERNARDES, N. C., BONILLA, A., MÜLLER, V., & PERIS, A. (2014). Li–Yorke chaos in linear dynamics. Ergodic Theory and Dynamical Systems, 35(6), 1723-1745. doi:10.1017/etds.2014.20Conejero, J. A., Murillo-Arcila, M., & Seoane-Sepúlveda, J. B. (2015). Linear chaos for the Quick-Thinking-Driver model. Semigroup Forum, 92(2), 486-493. doi:10.1007/s00233-015-9704-6On kinematic waves II. A theory of traffic flow on long crowded roads. (1955). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 229(1178), 317-345. doi:10.1098/rspa.1955.0089Jordan, P. M., & Feuillade, C. (2006). On the propagation of transient acoustic waves in isothermal bubbly liquids. Physics Letters A, 350(1-2), 56-62. doi:10.1016/j.physleta.2005.10.004Alberto Conejero, J., Rodenas, F., & Trujillo, M. (2015). Chaos for the Hyperbolic Bioheat Equation. Discrete & Continuous Dynamical Systems - A, 35(2), 653-668. doi:10.3934/dcds.2015.35.653Bonet, J., & Peris, A. (1998). Hypercyclic Operators on Non-normable Fréchet Spaces. Journal of Functional Analysis, 159(2), 587-595. doi:10.1006/jfan.1998.3315Jordan, P. M. (2004). An analytical study of Kuznetsov’s equation: diffusive solitons, shock formation, and solution bifurcation. Physics Letters A, 326(1-2), 77-84. doi:10.1016/j.physleta.2004.03.067Bayart, F. (2010). Dynamics of holomorphic groups. Semigroup Forum, 82(2), 229-241. doi:10.1007/s00233-010-9284-4Conejero, J. A., Müller, V., & Peris, A. (2007). Hypercyclic behaviour of operators in a hypercyclic C0-semigroup. Journal of Functional Analysis, 244(1), 342-348. doi:10.1016/j.jfa.2006.12.008Richards, P. I. (1956). Shock Waves on the Highway. Operations Research, 4(1), 42-51. doi:10.1287/opre.4.1.42Ansari, S. I. (1995). Hypercyclic and Cyclic Vectors. Journal of Functional Analysis, 128(2), 374-383. doi:10.1006/jfan.1995.1036Rudnicki, R. (2012). Chaoticity and invariant measures for a cell population model. Journal of Mathematical Analysis and Applications, 393(1), 151-165. doi:10.1016/j.jmaa.2012.03.055El Mourchid, S., Metafune, G., Rhandi, A., & Voigt, J. (2008). On the chaotic behaviour of size structured cell populations. Journal of Mathematical Analysis and Applications, 339(2), 918-924. doi:10.1016/j.jmaa.2007.07.034BANASIAK, J., & LACHOWICZ, M. (2002). TOPOLOGICAL CHAOS FOR BIRTH-AND-DEATH-TYPE MODELS WITH PROLIFERATION. Mathematical Models and Methods in Applied Sciences, 12(06), 755-775. doi:10.1142/s021820250200188xConejero, J. A., & Peris, A. (2005). Linear transitivity criteria. Topology and its Applications, 153(5-6), 767-773. doi:10.1016/j.topol.2005.01.009Jordan, P. M., Keiffer, R. S., & Saccomandi, G. (2014). Anomalous propagation of acoustic traveling waves in thermoviscous fluids under the Rubin–Rosenau–Gottlieb theory of dispersive media. Wave Motion, 51(2), 382-388. doi:10.1016/j.wavemoti.2013.08.009Mourchid, S. E. (2006). The Imaginary Point Spectrum and Hypercyclicity. Semigroup Forum, 73(2), 313-316. doi:10.1007/s00233-005-0533-xOprocha, P. (2006). A quantum harmonic oscillator and strong chaos. Journal of Physics A: Mathematical and General, 39(47), 14559-14565. doi:10.1088/0305-4470/39/47/003Shkarin, S. (2011). On supercyclicity of operators from a supercyclic semigroup. Journal of Mathematical Analysis and Applications, 382(2), 516-522. doi:10.1016/j.jmaa.2010.08.033Emamirad, H. (1998). Hypercyclicity in the scattering theory for linear transport equation. Transactions of the American Mathematical Society, 350(9), 3707-3716. doi:10.1090/s0002-9947-98-02062-5Kalisch, G. K. (1972). On operators on separable Banach spaces with arbitrary prescribed point spectrum. Proceedings of the American Mathematical Society, 34