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Smale diffeomorphisms and surface topology

Published online by Cambridge University Press:  19 September 2008

Steve Batterson
Affiliation:
Department of Mathematics, Emory University, Atlanta, Georgia 30322, USA
John Smillie
Affiliation:
Department of Mathematics, Herbert H. Lehman College, CUNY, Bronx, NY 10468, USA and Mathematical Sciences Research Institute, University of California, Berkeley, CA 94720, USA
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Abstract

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This paper concerns Smale diffeomorphisms of compact oriented surfaces. Relationships are found between the isotopy class of the map and the dynamics of its basic sets. The form of the dynamical properties involves restrictions on periods and reduced zeta functions.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1985

References

[B-F]Blanchard, P. & Franks, J.. An obstruction to the existence of certain dynamics in surface diffeomorphisms. Ergod. Th. & Dynam. Sys. 1 (1981), 255260.CrossRefGoogle Scholar
[B-S]Batterson, S. & Smillie, J.. Filtrations and periodic data on surfaces. To appear in Amer. Jour. Math.Google Scholar
[F]Franks, J.. Homology and Dynamical Systems. CBMS Regional Conf. Series, 49 (1982).CrossRefGoogle Scholar
[Fr]Fried, D.. Subshifts on surfaces. Ergod. Th. & Dynam. Sys. 2 (1982), 1521.CrossRefGoogle Scholar
[J-S]Jaco, W. & Shalen, P.. Surface homeomorphisms and periodicity. Topology 16 (1977), 347367.CrossRefGoogle Scholar
[W]Williams, R.. Classification of subshifts of finite type. Ann. of Math. 98 (1973), 120153CrossRefGoogle Scholar
Errata 99 (1979), 370–381.Google Scholar
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