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Entropy and semi-conjugacy in dimension two

Published online by Cambridge University Press:  19 September 2008

Michael Handel
Michael Handel
Affiliation:
Department of Mathematics and Computer Science, Lehman College, Bronx, New York 10468, USA
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Abstract

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We prove that if a diffeomorphism f of a closed surface is homotopic to and has the same topological entropy as a pseudo-Anosov homeomorphism g, then f is semi-conjugate to g. As part of the proof, a necessary and sufficient condition is given for a pseudo-orbit of a pseudo-Anosov homeomorphism g to be shadowed by an actual orbit of g.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Issue 4 , December 1988 , pp. 585 - 596
Copyright
Copyright © Cambridge University Press 1988

References

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