New chaos indicators for systems with extremely small Lyapunov exponents

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 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.