In:
Journal of the Australian Mathematical Society, Cambridge University Press (CUP), Vol. 98, No. 3 ( 2015-06), p. 375-389
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.
Type of Medium:
Online Resource
ISSN:
1446-7887
,
1446-8107
DOI:
10.1017/S1446788714000640
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2015
detail.hit.zdb_id:
1478743-X
SSG:
17,1
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