803 research outputs found

    Nambu-Hamiltonian flows associated with discrete maps

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    For a differentiable map (x1,x2,...,xn)→(X1,X2,...,Xn)(x_1,x_2,..., x_n)\to (X_1,X_2,..., X_n) that has an inverse, we show that there exists a Nambu-Hamiltonian flow in which one of the initial value, say xnx_n, of the map plays the role of time variable while the others remain fixed. We present various examples which exhibit the map-flow correspondence.Comment: 19 page

    Cryptographic requirements for chaotic secure communications

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    In recent years, a great amount of secure communications systems based on chaotic synchronization have been published. Most of the proposed schemes fail to explain a number of features of fundamental importance to all cryptosystems, such as key definition, characterization, and generation. As a consequence, the proposed ciphers are difficult to realize in practice with a reasonable degree of security. Likewise, they are seldom accompanied by a security analysis. Thus, it is hard for the reader to have a hint about their security. In this work we provide a set of guidelines that every new cryptosystems would benefit from adhering to. The proposed guidelines address these two main gaps, i.e., correct key management and security analysis, to help new cryptosystems be presented in a more rigorous cryptographic way. Also some recommendations are offered regarding some practical aspects of communications, such as channel noise, limited bandwith, and attenuation.Comment: 13 pages, 3 figure

    Renormalization Group Functional Equations

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    Functional conjugation methods are used to analyze the global structure of various renormalization group trajectories, and to gain insight into the interplay between continuous and discrete rescaling. With minimal assumptions, the methods produce continuous flows from step-scaling {\sigma} functions, and lead to exact functional relations for the local flow {\beta} functions, whose solutions may have novel, exotic features, including multiple branches. As a result, fixed points of {\sigma} are sometimes not true fixed points under continuous changes in scale, and zeroes of {\beta} do not necessarily signal fixed points of the flow, but instead may only indicate turning points of the trajectories.Comment: A physical model with a limit cycle added as section IV, along with reference

    No Time Machine Construction in Open 2+1 Gravity with Timelike Total Energy Momentum

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    It is shown that in 2+1 dimensional gravity an open spacetime with timelike sources and total energy momentum cannot have a stable compactly generated Cauchy horizon. This constitutes a proof of a version of Kabat's conjecture and shows, in particular, that not only a Gott pair cannot be formed from processes such as the decay of a single cosmic string as has been shown by Carroll et al., but that, in a precise sense, a time machine cannot be constructed at all.Comment: 7 pages. Several changes and 3 figures added. To appear in Phys. Rev.

    Plykin-like attractor in non-autonomous coupled oscillators

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    A system of two coupled non-autonomous oscillators is considered. Dynamics of complex amplitudes is governed by differential equations with periodic piecewise continuous dependence of the coefficients on time. The Poincar\'{e} map is derived explicitly. With exclusion of the overall phase, on which the evolution of other variables does not depend, the Poincar\'{e} map is reduced to 3D mapping. It possesses an attractor of Plykin type located on an invariant sphere. Computer verification of the cone criterion confirms the hyperbolic nature of the attractor in the 3D map. Some results of numerical studies of the dynamics for the coupled oscillators are presented, including the attractor portraits, Lyapunov exponents, and the power spectral density.Comment: 11 pages, 9 figure
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