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CHAIN COMPONENTS WITH THE STABLE SHADOWING PROPERTY FOR C1 VECTOR FIELDS
Journal of the Australian Mathematical Society  (IF0.8),  Pub Date : 2021-02-01, DOI: 10.1017/s1446788720000415
MANSEOB LEE, LE HUY TIEN

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.