Stickiness and recurrence plots: an entropy-based approach

TL;DR

This paper introduces an entropy-based measure derived from recurrence plots to analyze the dynamics of quasi-integrable Hamiltonian systems, effectively distinguishing between regular and chaotic behaviors and revealing hierarchical structures.

Contribution

It proposes the recurrence time entropy (RTE) as a novel metric to characterize system dynamics and demonstrates its correlation with Lyapunov exponents and hierarchical phase space structures.

Findings

RTE correlates strongly with the largest Lyapunov exponent

Multi-modal RTE distribution reflects hierarchical island structures

RTE effectively distinguishes regular and chaotic regions

Abstract

The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and find that each mode corresponds to the motion around islands of different hierarchical levels.