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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
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