Mixing and relaxation dynamics of the Henon map at the edge of chaos

TL;DR

This paper investigates the mixing and relaxation behaviors of the Henon map at the edge of chaos, confirming weak chaos characteristics in a two-dimensional system and extending previous one-dimensional findings.

Contribution

It provides the first numerical verification of weak mixing and chaos in the two-dimensional Henon map at the edge of chaos, linking these concepts to nonextensive thermostatistics.

Findings

Results align with one-dimensional dissipative maps

First verification of weak mixing in 2D Henon map

Supports the concept of weak chaos at the edge of chaos

Abstract

The mixing properties (or sensitivity to initial conditions) and relaxation dynamics of the Henon map, together with the connection between these concepts, have been explored numerically at the edge of chaos. It is found that the results are consistent with those coming from one-dimensional dissipative maps. This constitutes the first verification of the scenario in two-dimensional cases and obviously reinforces the idea of weak mixing and weak chaos. Keywords: Nonextensive thermostatistics, Henon map, dynamical systems