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Rotation and periodicity in plane separating continua

Published online by Cambridge University Press:  19 September 2008

Marcy Barge  and
Richard M. Gillette
Marcy Barge
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717, USA
Richard M. Gillette
Affiliation:
Department of Mathematical Sciences, Montana State University, Bozeman, Montana 59717, USA
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Abstract

We prove that if F is an orientation-preserving homeomorphism of the plane that leaves invariant a continuum Λ which irreducibly separates the plane into exactly two domains, then the convex hull of the rotation set of F restricted to Λ is a closed interval and each reduced rational in this interval is the rotation number of a periodic orbit in Λ. We also show that the interior and exterior rotation numbers of F associated with Λ are contained in the convex hull of the rotation set of F restricted to Λ and that if this set is nondegenerate then Λ is an indecomposable continuum.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 4 , December 1991 , pp. 619 - 631
Copyright
Copyright © Cambridge University Press 1991

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