145 research outputs found
Basin of attraction of triangular maps with applications
We consider some planar triangular maps. These maps preserve certain
fibration of the plane. We assume that there exists an invariant attracting
fiber and we study the limit dynamics of those points in the basin of
attraction of this invariant fiber, assuming that either it contains a global
attractor, or it is filled by fixed or 2-periodic points. Finally, we apply our
results to a variety of examples, from particular cases of triangular systems
to some planar quasi-homogeneous maps, and some multiplicative and additive
difference equations, as well.Comment: 1 figur
Fixed Point Properties of the Ising Ferromagnet on the Hanoi Networks
The Ising model with ferromagnetic couplings on the Hanoi networks is
analyzed with an exact renormalization group. In particular, the fixed-points
are determined and the renormalization-group flow for certain initial
conditions is analyzed. Hanoi networks combine a one-dimensional lattice
structure with a hierarchy of small-world bonds to create a mix of geometric
and mean-field properties. Generically, the small-world bonds result in
non-universal behavior, i.e. fixed points and scaling exponents that depend on
temperature and the initial choice of coupling strengths. It is shown that a
diversity of different behaviors can be observed with seemingly small changes
in the structure of the networks. Defining interpolating families of such
networks, we find tunable transitions between regimes with power-law and
certain essential singularities in the critical scaling of the correlation
length, similar to the so-called inverted Berezinskii-Kosterlitz-Thouless
transition previously observed only in scale-free or dense networks.Comment: 13 pages, revtex, 12 fig. incl.; fixed confusing labels, published
version. For related publications, see
http://www.physics.emory.edu/faculty/boettcher
The IR stability of de Sitter QFT: results at all orders
We show that the Hartle-Hawking vacuum for theories of interacting massive
scalars in de Sitter space is both perturbatively well-defined and stable in
the IR. Correlation functions in this state may be computed on the Euclidean
section and Wick-rotated to Lorentz-signature. The results are manifestly de
Sitter-invariant and contain only the familiar UV singularities. More
importantly, the connected parts of all Lorentz-signature correlators decay at
large separations of their arguments. Our results apply to all cases in which
the free Euclidean vacuum is well defined, including scalars with masses
belonging to both the complementary and principal series of . This
suggests that interacting QFTs in de Sitter -- including higher spin fields --
are perturbatively IR-stable at least when i) the Euclidean vacuum of the
zero-coupling theory exists and ii) corresponding Lorentz-signature
zero-coupling correlators decay at large separations. This work has significant
overlap with a paper by Stefan Hollands, which is being released
simultaneously.Comment: 30 pp., 4 figures. Small typos fixed, refs adde
Asymptotic stability for block triangular maps
We prove a result concerning the asymptotic stability and the basin of attraction of fixed points for block triangular maps. This result is applied to some families of discrete dynamical systems and several types of difference equationsThis work is supported by the Ministry of Science and Innovation–State Research Agency of the Spanish Government through grants PID2019-104658 GBI00 and Severo Ochoa and Mar´ıa de Maeztu Program for Centers and Units of Excellence in R&D (CEX2020-001084-M) and also supported by the grants 2017SGR-1617 and 2017-SGR-388 from AGAUR, Generalitat de Catalunya.Peer ReviewedPostprint (published version
Calculation method for unstable periodic points in two-to-one maps using symbolic dynamical system
In this study, we have focused on the two-to-one maps and developed the numerical method to calculate the unstable periodic points (UPPs), based on the theory of the symbolic dynamical system. The core technique of the method is the definition of a non-deterministic map G. From the experimental result of three typical maps: logistic map, tent map, and Bernoulli map, we have confirmed the proposed method works very well within the defined errors. Our method has the following advantages: the method converges rapidly as the period of the target UPP is larger; we can choose the target UPP regardless of its cause (any bifurcation is not a matter); we can find the UPPs that are always unstable in the given parameter range. The convergence of the method is guaranteed by two standpoints: the corresponding symbolic dynamical system, and the asymptotic stability of UPP of G. Hereby, the error of the convergence is scalable according to the numeric precision of the software
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