Article Contents
Article Contents

Expansive and fixed point free homeomorphisms of the plane

• The aim of this work is to describe the set of fixed point free homeomorphisms of the plane (preserving orientation or not) under certain expansive conditions. We find necessary and sufficient conditions for a fixed point free homeomorphism of the plane to be topologically conjugate to a translation.
Mathematics Subject Classification: Primary: 37E30, 37D20; Secondary: 37B25.

 Citation:

•  [1] L. Brouwer, Beweis des ebenen Translationssatzes, Math. Ann., 72 (1912), 37-54.doi: 10.1007/BF01456888. [2] A. Fathi, Expansiveness, hyperbolicity and Hausdorff dimension, Commun. Math. Phys., 126 (1989), 249-262.doi: 10.1007/BF02125125. [3] J. Franks, A new proof of the Brouwer plane translation theorem, Ergod. Th. and Dynamic. Sys., 12 (1991), 217-226. [4] Jorge Groisman, "Expansive Homeomorphisms of the Plane," Ph.D. thesis, Universidad de la República, Uruguay, 2007. [5] J. Groisman, Expansive homeomorphisms of the plane, Discrete and Continuous Dynam. Systems, 29 (2011), 213-239. [6] K. Hiraide, Expansive homeomorphisms of compact surfaces are pseudo-Anosov, Osaka J. Math., 27 (1990), 117-162. [7] K. Kuratowski, "Topology," Academic Press, New York-London, 1966. [8] J. Lewowicz, Expansive homeomorphisms of surfaces, Bol. Soc. Bras. Mat. (N.S.), 20 (1989), 113-133. [9] W. White, An Anosov translation, in "Dynamical Systems" (Proc. Sympos., Univ. of Bahia, Salvador, 1971), Academic Press, New York, (1973), 667-670.