Hiraide, Koichi Expansive homeomorphisms of compact surfaces are pseudo-Anosov. (English) Zbl 0713.58042 Osaka J. Math. 27, No. 1, 117-162 (1990). 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 Cited in 35 Documents MSC: 37D99 Dynamical systems with hyperbolic behavior Keywords:C\({}^ 0\)-foliation; expansive homeomorphism; compact surface; pseudo- Anosov homeomorphism PDFBibTeX XMLCite \textit{K. Hiraide}, Osaka J. Math. 27, No. 1, 117--162 (1990; Zbl 0713.58042)