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February & March  2004, 11(2&3): 261-310. doi: 10.3934/dcds.2004.11.261

Smale diffeomorphisms of surfaces: a classification algorithm

François Béguin 1,

1. 

Université Paris Sud, Département de mathématiques, 91405 Orsay, France

Received  December 2002 Revised  January 2004 Published  June 2004

We are concerned here with Smale (i.e. $C^1$-structurally stable) diffeomorphisms of compact surfaces. Bonatti and Langevin have produced some combinatorial descriptions of the dynamics of any such diffeomorphism ([2]). Actually, each diffeomorphism admits infinitely many different combinatorial descriptions. The aim of the present article is to describe an algorithm which decides whether two combinatorial descriptions correspond to the same diffeomorphism or not. This provides an algorithmic way to classify Smale diffeomorphisms of surfaces up to topological conjugacy (on canonical neighbourhoods of the basic pieces).
Keywords: axiom A diffeomorphisms, Markov partitions., Smale diffeomorphisms.
Mathematics Subject Classification: 36C15, 37D20, 37E30.
Citation: François Béguin. Smale diffeomorphisms of surfaces: a classification algorithm. Discrete & Continuous Dynamical Systems, 2004, 11 (2&3) : 261-310. doi: 10.3934/dcds.2004.11.261
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