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In this paper we give a complete topological classification of orientationpreserving Morse-Smale diffeomorphisms on orientable closed surfaces. For MSdiffeomorphisms with relatively simple behaviour it was known that such aclassification can be given through a directed graph, a three-colour directedgraph or by a certain topological object, called a scheme. Here we will assignto any MS surface diffeomorphism a finite amount of data which completelydetermines its topological conjugacy class. Moreover, we show that associatedto any abstract version of this data, there exists a unique conjugacy class ofMS orientation preserving diffeomorphisms (on some orientation preservingsurface). As a corollary we obtain a different proof that nearby MSdiffeomorphisms are topologically conjugate.

A complete topological classification of Morse-Smale diffeomorphisms on surfaces: a kind of kneading theory in dimension two