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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
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