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HYPERBOLICITY OF HOMOCLINIC CLASSES OF
$C^{1}$ VECTOR FIELDS
Published online by Cambridge University Press: 21 November 2014
Abstract
Let ${\it\gamma}$ be a hyperbolic closed orbit of a
$C^{1}$ vector field
$X$ on a compact
$C^{\infty }$ manifold
$M$ and let
$H_{X}({\it\gamma})$ be the homoclinic class of
$X$ containing
${\it\gamma}$. In this paper, we prove that if a
$C^{1}$-persistently expansive homoclinic class
$H_{X}({\it\gamma})$ has the shadowing property, then
$H_{X}({\it\gamma})$ is hyperbolic.
MSC classification
- Type
- Research Article
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- Copyright
- © 2014 Australian Mathematical Publishing Association Inc.
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