Asymptotic Statistics of Poincar\'e Recurrences in Hamiltonian Systems with Divided Phase Space
Condensed Matter
2009-10-31 v1 chao-dyn
Chaotic Dynamics
Abstract
By different methods we show that for dynamical chaos in the standard map with critical golden curve the Poincar\'e recurrences P(\tau) and correlations C(\tau) asymptotically decay in time as P ~ C/\tau ~ 1/\tau^3. It is also explained why this asymptotic behavior starts only at very large times. We argue that the same exponent p=3 should be also valid for a general chaos border.
Keywords
Cite
@article{arxiv.cond-mat/9807365,
title = {Asymptotic Statistics of Poincar\'e Recurrences in Hamiltonian Systems with Divided Phase Space},
author = {B. V. Chirikov and D. L. Shepelyansky},
journal= {arXiv preprint arXiv:cond-mat/9807365},
year = {2009}
}
Comments
revtex, 4 pages, 3 ps-figures