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Expansive homeomorphisms of surfaces. (English) Zbl 0753.58022
The author’s abstract: “Let $$f$$ be an expansive homeomorphism of a compact oriented surface $$M$$. We show that $$S^ 2$$ does not support such an $$f$$, and that $$f$$ is conjugate to an Anosov diffeomorphism if $$M=\mathbb{T}^ 2$$, and to a pseudo-Anosov map if $$M$$ has genus $$\geq 2$$. These results are consequences of our description of local stable (unstable) sets: every $$x\in M$$ has a local stable (unstable) set that consists of the union of $$r$$ arcs that meet only at $$x$$. For each $$x\in M$$, $$r=2$$, except for a finite number of points, where $$r\geq 3$$”.

##### MSC:
 37D99 Dynamical systems with hyperbolic behavior
##### Keywords:
expansive homeomorphism; pseudo-Anosov map
Full Text:
##### References:
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