Periodic orbits and Arnold diffusion
نویسندگان
چکیده
منابع مشابه
Chaotic diffusion on periodic orbits: the perturbed Arnold cat map.
Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnold cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated, using the following PO formulas: (1). the curvature expansion of the Ruelle zeta function; (2). the average of the PO winding-numbe...
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We propose methods for constructing high-quality pseudorandom number generators (RNGs) based on an ensemble of hyperbolic automorphisms of the unit two-dimensional torus (Sinai-Arnold map or cat map) while keeping a part of the information hidden. The single cat map provides the random properties expected from a good RNG and is hence an appropriate building block for an RNG, although unnecessar...
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The goal of this paper is to present to non-specialists what is perhaps the simple possible geometrical picture explaining the mechanism of Arnold diffusion. We choose to speak of a specific model – that of geometric rays in a periodic optical medium. This model is equivalent to that of a particle in a periodic potential in R with energy prescribed and to the geodesic flow in a Riemannian metri...
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The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit actions are non-commensurable it is demonstrated by a few different methods that the spectral statistics of chaotic systems without time-reversal invariance in ...
متن کاملPeriodic Orbits and Zeta Functions
0. Introduction 1 1. Twisted orbits and zeta functions 3 2. Axiom A diieomorphisms 4 3. Symbolic dynamics and rationality 5 4. Zeta functions and for interval maps 9 5. The Ruelle zeta function 14 6. Zeta functions for hyperbolic ows 21 7. Zeta functions for analytic Anosov ows 25 8. L-functions and special values 26 9. counting closed orbits for ows 27 10. L-functions and homology 32 11. Pole ...
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ژورنال
عنوان ژورنال: Discrete and Continuous Dynamical Systems
سال: 2002
ISSN: 1078-0947
DOI: 10.3934/dcds.2003.9.451