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Characterization of MorseSmale isotopy classes on surfaces

Published online by Cambridge University Press:  19 September 2008

Luiz Fernando  and
C. Da Rocha
Luiz Fernando
Affiliation:
Instituto de Matemática da UFRGS, Porto Alegre, RS 90.000, Brazil
C. Da Rocha
Affiliation:
Instituto de Matemática da UFRGS, Porto Alegre, RS 90.000, Brazil
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Abstract

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In this paper we use Thurston's work on the dynamics of diffeomorphisms on surfaces to show that a diffeomorphism ƒ on a surface is isotopic to a Morse- Smale one if and only if the growth rate of the length of the words representing elements of the fundamental group under iteration by ƒ is one. Morse-Smale isotopy classes are also shown to be the same as Nielsen's algebraically finite type.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 1 , March 1985 , pp. 107 - 122
Copyright
Copyright © Cambridge University Press 1985

References

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