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Smale diffeomorphisms of surfaces: a classification algorithm
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).