Measure-Expansive Homoclinic Classes for C 1 Generic Flows

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

Mathematics, 2020, vol. 8, issue 8, 1-6

Abstract: In this paper, we prove that for a generically C 1 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.

Keywords: expansive; measure-expansive; homoclinic class; generic; hyperbolic (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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