Many intermingled basins in dimension 3

TL;DR

This paper constructs a class of diffeomorphisms on the 3-torus with multiple physical measures and intermingled basins, demonstrating complex dynamical behavior with hyperbolic properties.

Contribution

It introduces new examples of partially hyperbolic diffeomorphisms with arbitrary finite or countable physical measures and intermingled basins on -torus.

Findings

Existence of diffeomorphisms with any finite or countable number of physical measures

Examples are partially hyperbolic with specific splitting

Can be made volume hyperbolic and topologically mixing

Abstract

We construct a diffeomorphism of $\mathbb{T}^3$ admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting $T\mathbb{T}^3 = E^{cs} \oplus E^u$ and can be made volume hyperbolic and topologically mixing.