Chaotic diffusion on periodic orbits and uniformity

✍ Scribed by Itzhack Dana; Vladislav E Chernov

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 190 KB
• Volume: 330
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2003.08.011

✦ Synopsis

Chaotic di usion 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 di usion coe cient 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 su ciently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to uniformity sum rules satisÿed by the PO Lyapunov eigenvalues at ÿxed winding number.