2000/06/09 by Boris Chirikov, B. V. Chirikov, Chirikov, Boris
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Theoretical and Computational Physics #nlin.CD
paper · pdf · doi:10.48550/arxiv.nlin/0006013
Latex 2.09, 8 figures
arxiv created 2000/06/09 · openalex publication_date 2000/06/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The mechanism of the exponential transient statistics of Poincaré recurrences in the presence of chaos border with its critical structure is studied using two simple models: separatrix map and the kicked rotator ('microtron'). For the exponential transient to exist the two conditions have been shown to be crucial: fast (ballistic) relaxation, and a small measure of the critical structure. The latter was found to include a new peripheral part (halo) of a surprisingly large size. First preliminary empirical evidence is presented for a new regime of Poincaré recurrences including the transition from exponential to exponential statistics.