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On the non-robustness of intermingled basins

Published online by Cambridge University Press:  04 July 2016

RAÚL URES  and
CARLOS H. VÁSQUEZ
RAÚL URES
Affiliation:
IMERL, Facultad de Ingeniería, Universidad de la República, CC 30, Montevideo, Uruguay email ures@fing.edu.uy
CARLOS H. VÁSQUEZ
Affiliation:
Instituto de Matemática, Pontificia Universidad Católica de Valparaíso, Blanco Viel 596, Cerro Barón, Valparaíso, Chile email carlos.vasquez@ucv.cl
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 1 , February 2018 , pp. 384 - 400
Copyright
© Cambridge University Press, 2016 

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