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C1-STABLE INVERSE SHADOWING CHAIN COMPONENTS FOR GENERIC DIFFEOMORPHISMS
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 Title & Authors
C1-STABLE INVERSE SHADOWING CHAIN COMPONENTS FOR GENERIC DIFFEOMORPHISMS
Lee, Man-Seob;
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 Abstract
Let f be a diffeomorphism of a compact manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of -stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set of f has -stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) -generically, the chain component of f associated to p is hyperbolic if and only if has the -stable inverse shadowing property.
 Keywords
homoclinic class;-stable inverse shadowing;residual;generic;chain recurrent;chain component;hyperbolic;axiom A;
 Language
English
 Cited by
1.
Stably average shadowable homoclinic classes, Nonlinear Analysis: Theory, Methods & Applications, 2011, 74, 2, 689  crossref(new windwow)
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