Two-dimensional maps at the edge of chaos: Numerical results for the Henon map

TL;DR

This study numerically investigates the mixing properties of the two-dimensional Henon map at the edge of chaos using three methods, confirming the robustness of weak chaos scenarios in higher dimensions.

Contribution

First verification of weak chaos scenario in two-dimensional maps using multiple methods, extending previous one-dimensional results.

Findings

Results agree with one-dimensional cases

Confirms robustness of weak chaos in 2D maps

Uses three independent methods for analysis

Abstract

The mixing properties (or sensitivity to initial conditions) of two-dimensional Henon map have been explored numerically at the edge of chaos. Three independent methods, which have been developed and used so far for the one-dimensional maps, have been used to accomplish this task. These methods are (i)measure of the divergence of initially nearby orbits, (ii)analysis of the multifractal spectrum and (iii)computation of nonextensive entropy increase rates. The obtained results strongly agree with those of the one-dimensional cases and constitute the first verification of this scenario in two-dimensional maps. This obviously makes the idea of weak chaos even more robust.