Thick attractors with intermingled basins

TL;DR

This paper introduces new examples of dynamical systems with thick metric attractors that have intermingled basins, using random walks along orbits to develop the theory.

Contribution

It presents novel constructions of thick attractors with intermingled basins and develops the theoretical framework involving random walks along orbits.

Findings

Examples of thick metric attractors with intermingled basins are constructed.

Theoretical framework for random walks along orbits is developed.

New dynamical behaviors with intermingled basins are demonstrated.

Abstract

We construct various novel and elementary examples of dynamics with metric attractors that have intermingled basins. A main ingredient is the introduction of random walks along orbits of a given dynamical system. We develop theory for it and use it in particular to provide examples of thick metric attractors with intermingled basins.