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Wild Milnor attractors accumulated by lower-dimensional dynamics

Published online by Cambridge University Press:  05 November 2012

RAFAEL POTRIE*
Affiliation:
CMAT, Facultad de Ciencias, Universidad de la República, Uruguay LAGA, Institute Galilée, Universit́e Paris 13, Villetaneuse, France (email: rpotrie@cmat.edu.uy)

Abstract

We present new examples of open sets of diffeomorphisms such that generic diffeomorphisms in those sets have no dynamically indecomposable attractors in the topological sense and have infinitely many chain-recurrence classes. We show that all other classes except one are contained in periodic surfaces. This study allows us to obtain the existence of Milnor attractors as well as study ergodic properties of the diffeomorphisms in those open sets by using ideas and results from Bonatti and Viana [SRB measures for partially hyperbolic diffeomorphisms whose central direction is mostly contracting. Israel J. Math.115 (2000), 157–193] and Buzzi and Fisher [Entropic stability beyond partial hyperbolicity. Preprint, 2011, arXiv:1103:2707].

Type
Research Article
Copyright
Copyright © 2012 Cambridge University Press 

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