On a scenario of onset of strongly dissipative mixed dynamics

TL;DR

This paper explores the emergence of strongly dissipative mixed dynamics in two-dimensional reversible systems, focusing on vortex motion under perturbations, and identifies the role of homoclinic structures after crises.

Contribution

It presents a new scenario for the onset of mixed dynamics involving homoclinic structures in reversible diffeomorphisms with dissipative features.

Findings

Chaotic attractor intersects with chaotic repeller forming a thin set

Homoclinic structures emerge after crises of attractors and repellers

Scenario demonstrated using vortex motion system under perturbations

Abstract

In this paper we present the scenario of the occurrence of strongly dissipative mixed dynamics in two-dimensional reversible diffeomorphisms, using as an example the system describing a motion of two point vortices under the influence of wave perturbation and shear flow. For mixed dynamics of this type the chaotic attractor intersects with the chaotic repeller, but their intersection forms a "thin" set. The main stage of this scenario is the appearance of homoclinic structures for a symmetric saddle orbit which arise after crisis of a homoclinic attractor and repeller.