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December 2012 Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set
Takashi Shimomura
Tsukuba J. Math. 36(2): 173-183 (December 2012). DOI: 10.21099/tkbjm/1358776997

Abstract

Let f be a chain mixing continuous onto mapping from the Cantor set onto itself. Let g be an aperiodic homeomorphism on the Cantor set. We show that homeomorphisms that are topologically conjugate to g approximate f in the topology of uniform convergence if a trivial necessary condition on periodic points is satisfied. In particular, let f be a chain mixing continuous onto mapping from the Cantor set onto itself with a fixed point and g, an aperiodic homeomorphism on the Cantor set. Then, homeomorphisms that are topologically conjugate to g approximate f.

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Takashi Shimomura. "Aperiodic homeomorphisms approximate chain mixing endomorphisms on the Cantor set." Tsukuba J. Math. 36 (2) 173 - 183, December 2012. https://doi.org/10.21099/tkbjm/1358776997

Information

Published: December 2012
First available in Project Euclid: 21 January 2013

zbMATH: 1278.37019
MathSciNet: MR3058237
Digital Object Identifier: 10.21099/tkbjm/1358776997

Subjects:
Primary: 37B10, 54H20‎

Rights: Copyright © 2013 University of Tsukuba, Institute of Mathematics

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Vol.36 • No. 2 • December 2012
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