On measure expansive diffeomorphisms

Pacifico, M.; Vieitez, J.

doi:10.1090/S0002-9939-2014-12296-9

On measure expansive diffeomorphisms
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by M. J. Pacifico and J. L. Vieitez

Proc. Amer. Math. Soc. 143 (2015), 811-819

DOI: https://doi.org/10.1090/S0002-9939-2014-12296-9

Published electronically: October 17, 2014

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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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