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Exceptional minimal sets of C1+α-group actions on the circle

Published online by Cambridge University Press:  19 September 2008

S. Hurder
S. Hurder
Affiliation:
Department of Mathematics (M/C 249), University of Illinois at Chicago, PO Box 4348, Chicago, IL 60680, USA
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Abstract

We prove two extensions of Sacksteder's Theorem for the action A: Γ × S1 → S1 of a finitely-generated group Γ on the circle by C1+α-diffeomorphisms. If the action A has an exceptional minimal set K with a gap endpoint of exponential orbit growth rate, or if the action A on K has positive topological entropy, then the exceptional set K is hyperbolic. That is, A has a linearly contracting fixed-point in K. A key point of the paper is to prove a foliation closing lemma using the foliation geodesic flow technique.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 3 , September 1991 , pp. 455 - 467
Copyright
Copyright © Cambridge University Press 1991

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