极小李雅普诺夫指数系统的新混沌指标

arXiv: Chaotic Dynamics Pub Date : 2015-01-01 DOI:10.1142/9789813202740_0011

K. Okubo, K. Umeno

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摘要

我们提出了具有极小正李雅普诺夫指数系统的新的混沌指标。这些混沌指标首先可以检测Froeschl\'e映射的Arnold扩散区和Chirikov扩散区之间的急剧过渡，其次可以检测Lyapunov指数为零的系统中的混沌性，例如布尔变换和$S$-单峰函数，以表征次指数扩散。

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New chaos indicators for systems with extremely small Lyapunov exponents

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 Froeschl\'e 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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arXiv: Chaotic Dynamics

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