Expansive and fixed point free homeomorphisms of the plane

Jorge Groisman

doi:10.3934/dcds.2012.32.1709

Article Contents

2012, Volume 32, Issue 5: 1709-1721. Doi: 10.3934/dcds.2012.32.1709

This issue Previous Article Measure valued solutions of sub-linear diffusion equations with a drift term Next Article On a nonlocal parabolic problem arising in electrostatic MEMS control

Expansive and fixed point free homeomorphisms of the plane

Jorge Groisman^1,

1.
Instituto de Matemática y Estadística "Prof. Ing. Rafael Laguardia”, Facultad de Ingeniería, Julio Herrera y Reissig 565 11300, MONTEVIDEO

Received: November 2010

Revised: September 2011

Published: May 2012

Abstract Related Papers Cited by

Abstract

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.

Keywords:

Dynamical systems,
expansive homeomorphisms.

Mathematics Subject Classification: Primary: 37E30, 37D20; Secondary: 37B25.

Citation:

Related Papers

Cited by

References

[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.