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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Positive entropy homeomorphisms of chainable continua and indecomposable subcontinua


Author: Christopher Mouron
Journal: Proc. Amer. Math. Soc. 139 (2011), 2783-2791
MSC (2010): Primary 37B45, 37B40; Secondary 54F15
Published electronically: December 29, 2010
MathSciNet review: 2801619
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Abstract: It is shown that if $ X$ is a chainable continuum and $ h:X\longrightarrow X$ is a homeomorphism such that the topological entropy of $ h$ is greater than 0, then $ X$ must contain an indecomposable subcontinuum. This answers a question of Barge.


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Additional Information

Christopher Mouron
Affiliation: Department of Mathematics and Computer Science, Rhodes College, Memphis, Tennessee 38112
Email: mouronc@rhodes.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10783-9
PII: S 0002-9939(2010)10783-9
Keywords: Entropy, chainable continuum, indecomposable continuum
Received by editor(s): August 6, 2008
Received by editor(s) in revised form: July 20, 2010
Published electronically: December 29, 2010
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.