New chaos indicators for systems with extremely small Lyapunov exponents

2015/01/01 by K. Okubo, Ken-ichi Okubo, Okubo, Ken-ichi +2
Computer Science · Mathematics · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #nlin.CD

paper · pdf · doi:10.48550/arxiv.1501.00243

5 pages, 9 figures

openalex publication_date 2015/01/01 · arxiv created 2015/03/18 · arxiv updated 2015/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose new chaos indicators for systems with extremely small positive Lyapunov exponents. These chaos indicators can firstly detect a sharp transition between the Arnold diffusion regime and the Chirikov diffusion regime of the Froeschlé map and secondly detect chaoticity in systems with zero Lyapunov exponent such as the Boole transformation and the S-unimodal function to characterize sub-exponential diffusions.

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