Michael Field.

Equivariant diffeomorphisms hyperbolic transverse to a G-action

Let G be a compact Lie group acting smoothly on a compact differential manifold and suppose that all G-orbits have the same dimension. We say that a G-equivariant diffeomorphism is G-Anosov if it is hyperbolic transverse to the G-action. We prove that G-Anosov diffeomorphisms are G-structurally stable and form an open subset of the group of equivariant diffeomorphisms. We prove similar results for flows.

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