Abstract:Let f : M → M be a diffeomorphism on a closed smooth n(n 2)-dimensional manifold M and let p be a hyperbolic periodic point of f. We show that if the homoclinic class H f (p) is R-robustly measure expansive then it is hyperbolic.
In this paper, we prove that for a generically C1 vector field X of a compact smooth manifold M, if a homoclinic class H(γ,X) which contains a hyperbolic closed orbit γ is measure expansive for X then H(γ,X) is hyperbolic.
In this paper, we prove that for a generically C1 vector field X of a compact smooth manifold M, if a homoclinic class H(γ,X) which contains a hyperbolic closed orbit γ is measure expansive for X then H(γ,X) is hyperbolic.
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