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Expansive homeomorphisms of compact surfaces are pseudo-Anosov. (English) Zbl 0713.58042
The paper contains a proof of the following Theorem: Every expansive homeomorphism of a compact surface is a pseudo-Anosov homeomorphism. The notion of pseudo-Anosov is well-known for diffeomorphisms, an appropriate definition for homeomorphisms is given in the paper. The author claims that the above result combined with Euler-PoincarĂ©’s formula and Kneser’s Theorem gives the following: There exist no expansive homeomorphisms on the 2-sphere, the projective plane and the Klein bottle.
Reviewer: J.Ombach

MSC:
37D99 Dynamical systems with hyperbolic behavior
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