Chaotic diffusion on periodic orbits and uniformity

Itzhack Dana and Vladislav E Chernov

Physica A: Statistical Mechanics and its Applications, 2003, vol. 330, issue 1, 253-258

Abstract: Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd cat map, exhibiting a transition from uniform to nonuniform hyperbolicity as the perturbation parameter is increased. The results for the diffusion coefficient from PO formulas agree very well with those obtained by standard methods. Using the original PO formula involving a uniform (nonweighted) average over the POs, reasonably accurate results are obtained for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to uniformity sum rules satisfied by the PO Lyapunov eigenvalues at fixed winding number.

Keywords: Chaotic diffusion; Periodic orbits; Hyperbolic Hamiltonian systems; Arnol'd cat map; Structural stability (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:330:y:2003:i:1:p:253-258

DOI: 10.1016/j.physa.2003.08.011

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