Wild Milnor attractors accumulated by lower dimensional dynamics

TL;DR

This paper constructs examples of diffeomorphisms with complex attractor structures, including infinitely many chain-recurrence classes and Milnor attractors, revealing intricate dynamics in lower-dimensional systems.

Contribution

It introduces new open sets of diffeomorphisms with unique attractor properties and analyzes their ergodic behavior using advanced dynamical systems techniques.

Findings

Existence of Milnor attractors in the constructed systems

Presence of infinitely many chain-recurrence classes

Most classes are contained in periodic surfaces

Abstract

We present new examples of open sets of diffeomorphisms such that a generic diffeomorphisms in those sets have no dynamically indecomposable attractors in the topological sense and have infinitely many chain-recurrence classes. We show that except from one particular class, the other classes are contained in periodic surfaces. This study allows us to obtain existence of Milnor attractors as well as studying ergodic properties of the diffeomorphisms in those open sets by using the ideas and results from [BV] and [BF].