Smale diffeomorphisms of surfaces: a classification algorithm | Zendy

François Béguin | Zendy

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Smale diffeomorphisms of surfaces: a classification algorithm

Author(s) -

François Béguin

Publication year - 2004

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2004.11.261

Subject(s) - diffeomorphism , topological conjugacy , conjugacy class , algorithm , computer science , surface (topology) , mathematics , topology (electrical circuits) , pure mathematics , geometry , combinatorics

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).

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