Do Chaotic Trajectories Care About Self-Similarity?

Details Do Chaotic Trajectories Care About Self-Similarity? Do Chaotic Trajectories Care About Self-Similarity?

2001-06-15

arxiv.org/abs/nlin/0106021v2

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures, minor corrections to previous version

Scientific paper

We investigate the relation between the chaotic dynamics and the hierarchical phase-space structure of generic Hamiltonian systems. We demonstrate that even in ideal situations when the phase space is dominated by an exactly self-similar structure, the long-time dynamics is {\it not} dominated by this structure. This has consequences for the power-law decay of correlations and Poincar\'e recurrences.

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