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

 

The pseudo-orbit tracing property and expansiveness on the Cantor set


Author: Takashi Shimomura
Journal: Proc. Amer. Math. Soc. 106 (1989), 241-244
MSC: Primary 58F15; Secondary 54H20, 58F13
MathSciNet review: 942637
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Abstract: The set of all the expansive homeomorphisms with the pseudo-orbit tracing property is dense in the space of all the homeomorphisms of the Cantor set with the topology of uniform convergence. Moreover a topologically transitive (resp. mixing) homeomorphism of the Cantor set is approximated uniformly by topologically transitive (resp. mixing) expansive homeomorphisms with the pseudo-orbit tracing property.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0942637-2
PII: S 0002-9939(1989)0942637-2
Keywords: Cantor set, homeomorphism, the pseudo-orbit tracing property, expansive, subshift of finite type, subshift
Article copyright: © Copyright 1989 American Mathematical Society