On the non-robustness of intermingled basins

Abstract

It is well-known that it is possible to construct a partially hyperbolic diffeomorphism on the 3-torus in a similar way than in 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 basins phenomenon for diffeomorphisms defined on boundaryless manifolds? In this work we will show that on the 3-torus the only partially hyperbolic examples having hyperbolic physical measures with intermingled basins are not robust