R-robustly measure expansive homoclinic classes are hyperbolic

Authors

Manseob Lee - Department of Mathematics, Mokwon University, Daejeon, 302-729, Korea

Abstract

Let \(f:M\to M\) be a diffeomorphism on a closed smooth \(n(n\geq 2)\)-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.

Keywords

Expansive, measure expansive, local product structure, shadowing, hyperbolic, homoclinic class, generic

References

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