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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.
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- Research Article
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- © 2014 Australian Mathematical Publishing Association Inc.
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