On 2-diffeomorphisms with one-dimensional basic sets and a finite number of moduli
This paper is a step towards the complete topological classication of omega-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and suffcient conditions for two such dieomorphisms to be topologically conjugate without assuming that the dieomorphisms are necessarily close to each other. In this paper we will establish such a classication within a certain class of omega-stable dieomorphisms de-ned below. To determine whether two diffeomorphisms from this class are topologically conjugate, we give (i) an algebraic description of the dynamics on their non-trivial basic sets, (ii) a geometric description of how invariant manifolds intersect, and (iii) dene numerical invariants, called moduli, associated to orbits of tangency of stable and unstable manifolds of saddle periodic orbits. This description determines the scheme of a diffeomorphism, and we will show that two diffeomorphisms from the class are topologically conjugate if and only if their schemes agree.