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CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C1 VECTOR FIELDS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 110 / Issue 2 / April 2021
- Published online by Cambridge University Press:
- 01 February 2021, pp. 243-259
- Print publication:
- April 2021
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- Article
- Export citation
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Let M be a closed n-dimensional smooth Riemannian manifold, and let X be a
$C^1$-vector field of 
$M.$ Let 
$\gamma $ be a hyperbolic closed orbit of 
$X.$ In this paper, we show that X has the 
$C^1$-stably shadowing property on the chain component 
$C_X(\gamma )$ if and only if 
$C_X(\gamma )$ is the hyperbolic homoclinic class.
