On the non-robustness of intermingled basins

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Abstract

It is well known that it is possible to construct a partially hyperbolic diffeomorphism on the 3-torus in a similar way to Kan's example. It has two hyperbolic physical measures with intermingled basins supported on two embedded tori with Anosov dynamics. A natural question is how robust is the intermingled basin phenomenon for diffeomorphisms defined on boundaryless manifolds? In this work we study partially hyperbolic diffeomorphisms on the 3-torus and show that the intermingled basin phenomenon is not robust.

Original languageEnglish
Pages (from-to)384-400
Number of pages17
JournalErgodic Theory and Dynamical Systems
Volume38
Issue number1
DOIs
StatePublished - 1 Feb 2018

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