Chaotic diffusion on periodic orbits and uniformity

Itzhack Dana, Vladislav E. Chernov

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations

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.

Original languageEnglish
Pages (from-to)253-258
Number of pages6
JournalPhysica A: Statistical Mechanics and its Applications
Volume330
Issue number1-2
DOIs
StatePublished - 1 Dec 2003
EventRandomes and Complexity - Eilat, Israel
Duration: 5 Jan 20039 Jan 2003

Bibliographical note

Funding Information:
We thank J.M. Robbins for discussions. This work was partially supported by the Israel Science Foundation administered by the Israel Academy of Sciences and Humanities. V.E.C. acknowledges the CRDF and Ministry of Education of the Russian Federation for Award #VZ-010-0.

Keywords

  • Arnol'd cat map
  • Chaotic diffusion
  • Hyperbolic Hamiltonian systems
  • Periodic orbits
  • Structural stability

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