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Mather invariants and smooth conjucacy on $$\mathbb S^2$$. (English) Zbl 1063.37036
Summary: We construct a “Mather invariant” for certain classes of diffeomorphisms of the sphere. We show that two such maps $$f$$ and $$g$$ are smoothly conjugate if and only if the eigenvalues of $$Df$$ and $$Dg$$ at the fixed points agree and the Mather invariants are equivalent. We also show that the Mather invariant is onto as a functional and give conditions on the invariant under which a diffeomorphism is embeddable in a flow.
##### MSC:
 37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces 37C15 Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems 58K65 Topological invariants on manifolds
##### Keywords:
heteroclinic orbit; smooth invariant
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