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arXiv · 1302.2282

On measure expansive diffeomorphisms

Maria Jose Pacifico·Jose L. Vieitez
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Abstract

Let $f: M \to M$ be a diffeomorphism defined on a compact boundaryless $d$-dimensional manifold $M$, $d\geq 2$. C. Morales has proposed the notion of measure expansiveness. 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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Maria Jose Pacifico, Jose L. Vieitez. 2013-02-10. On measure expansive diffeomorphisms. https://arxiv.org/abs/1302.2282

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