Abstract
AbstractLetpbe a hyperbolic periodic saddle of a diffeomorphismfon a closed$C^\infty $manifoldM, and letCf(p) be the chain component offcontainingp. In this paper, we show that ifCf(p) isC1-stably shadowable, then (i) Cf(p) is the homoclinic class ofpand admits a dominated splitting$E \oplus F$(where the dimension ofEis equal to that of the stable eigenspace ofp); (ii) theCf(p)-germ offis expansive if and only ifCf(p) is hyperbolic; and (iii) whenMis a surface,Cf(p) is locally maximal if and only ifCf(p) is hyperbolic.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
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