Many intermingled basins in dimension 3
Christian Bonatti, Rafael Potrie

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 admitting any finite or countable number of physical measures with intermingled basins. The examples are partially hyperbolic with splitting and can be made volume hyperbolic and topologically mixing.
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