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On measure expansive diffeomorphisms


Authors: M. J. Pacifico and J. L. Vieitez
Journal: Proc. Amer. Math. Soc. 143 (2015), 811-819
MSC (2010): Primary 37C29, 37D30
DOI: https://doi.org/10.1090/S0002-9939-2014-12296-9
Published electronically: October 17, 2014
MathSciNet review: 3283667
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Abstract: Let $ f: M \to M$ be a diffeomorphism defined on a compact boundaryless $ d$-dimensional manifold $ M$, $ d\geq 2$. In this note we show that diffeomorphisms in a residual subset far from homoclinic tangencies are measure expansive. We also show that surface diffeomorphisms presenting homoclinic tangencies can be $ C^1$-approximated by non-measure expansive diffeomorphisms.


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Additional Information

M. J. Pacifico
Affiliation: Instituto de Metematica, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, RJ, Brazil
Email: pacifico@im.ufrj.br

J. L. Vieitez
Affiliation: Instituto de Matematica, Facultad de Ingenieria, Universidad de la Republica, CC30, CP 11300, Montevideo, Uruguay
Email: jvieitez@fing.edu.uy

DOI: https://doi.org/10.1090/S0002-9939-2014-12296-9
Received by editor(s): February 12, 2013
Received by editor(s) in revised form: March 2, 2013, and June 6, 2013
Published electronically: October 17, 2014
Additional Notes: The first author was partially supported by CNPq Brazil, Pronex on Dynamical Systems, FAPERJ, Balzan Research Project of J. Palis
The second author was partially supported by Grupo de Investigación “Sistemas Dinámicos” CSIC (Universidad de la República), SNI-ANII, PEDECIBA, Uruguay
Communicated by: Nimish Shah
Article copyright: © Copyright 2014 American Mathematical Society

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