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Homeomorphic restrictions of smooth endomorphisms of an interval

Published online by Cambridge University Press:  19 September 2008

Karen M. Brucks ,
Maria Victoria Otero-Espinar  and
Charles Tresser
Karen M. Brucks
Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
Maria Victoria Otero-Espinar
Affiliation:
Departamento de Analise Matematica, Facultade de Matematicas, Campus Universitario, s/n. 15771 Santiago de Compostea, Spain
Charles Tresser
Affiliation:
IBM, T. J. Watson Research Center, Yorktown Heights, NY 10598, USA
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Abstract

We describe the asymptotic dynamics of homeomorphisms obtained as restrictions of generic C2 endomorphisms of an interval with finitely many critical points, all of which are non-flat, and with all periodic points hyperbolic. The ω -limit set of such a restricted endomorphism cannot be infinite, except when the restriction of the endomorphism to the closure of the orbit of some critical point is a minimal homeomorphism of an infinite set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 3 , September 1992 , pp. 429 - 439
Copyright
Copyright © Cambridge University Press 1992

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