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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

A transitive homeomorphism on the pseudoarc which is semiconjugate to the tent map


Author: Judy Kennedy
Journal: Trans. Amer. Math. Soc. 326 (1991), 773-793
MSC: Primary 54F15; Secondary 54C10, 54F50, 54H20
MathSciNet review: 1010412
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Abstract: A powerful theorem and construction of Wayne Lewis are used to build two homeomorphisms on the pseudoarc, each of which is semiconjugate to the tent map on the unit interval. The first homeomorphism is transitive, thus answering a question of Marcy Barge as to whether such homeomorphisms exist. The second homeomorphism admits wandering points. Also, it is proven that any homeomorphism on the pseudoarc that is semiconjugate to the tent map and is irreducible with respect to the semiconjugacy must either be transitive or admit wandering points.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1010412-2
PII: S 0002-9947(1991)1010412-2
Keywords: Pseudoarc, wandering point, transitive homeomorphism, indecomposable continuum, tent map, semiconjugate, chainable continuum
Article copyright: © Copyright 1991 American Mathematical Society