Nonwandering structures at the perioddoubling limit in dimensions and
Authors:
Marcy M. Barge and Russell B. Walker
Journal:
Trans. Amer. Math. Soc. 337 (1993), 259277
MSC:
Primary 58F12; Secondary 54H20, 58F13
MathSciNet review:
1161425
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Abstract: A Cantor set supporting an adding machine is the simplest nonwandering structure that can occur at the conclusion of a sequence of perioddoubling bifurcations of plane homeomorphisms. In some families this structure is persistent. In this manuscript it is shown that no plane homeomorphism has nonwandering Knaster continua on which the homeomorphism is semiconjugate to the adding machine. Using a theorem of M. Brown, a threespace homeomorphism is constructed which has an invariant set, , the product of a Knaster continuum and a Cantor set. is chainable, supports positive entropy but contains only poweroftwo periodic orbits. And the homeomorphism restricted to is semiconjugate to the adding machine. Lastly, a zero topological entropy disk diffeomorphism is constructed which has large nonwandering structures over a generalized adding machine on a Cantor set.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947199311614253
PII:
S 00029947(1993)11614253
Article copyright:
© Copyright 1993 American Mathematical Society
