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C1-stably shadowable chain components


Let p be a hyperbolic periodic saddle of a diffeomorphism f on a closed manifold M, and let Cf(p) be the chain component of f containing p. In this paper, we show that if Cf(p) is C1-stably shadowable, then (i) Cf(p) is the homoclinic class of p and admits a dominated splitting (where the dimension of E is equal to that of the stable eigenspace of p); (ii) the Cf(p)-germ of f is expansive if and only if Cf(p) is hyperbolic; and (iii) when M is a surface, Cf(p) is locally maximal if and only if Cf (p) is hyperbolic.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
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