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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Entropy and exponential growth of $ \pi\sb 1$ in dimension two


Authors: John M. Franks and Michael Handel
Journal: Proc. Amer. Math. Soc. 102 (1988), 753-760
MSC: Primary 58F15; Secondary 28D20, 58F11
MathSciNet review: 929016
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Abstract: The authors show that if $ f:M \to M$ is a $ {C^{1 + \alpha }}$ diffeomorphism of a compact surface and if the topological entropy of $ f$ is positive then there is a finite invariant set $ P$ such that the map induced by $ f$ on $ {\pi _1}(M - P)$ has exponential growth.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0929016-8
PII: S 0002-9939(1988)0929016-8
Article copyright: © Copyright 1988 American Mathematical Society