C1-STABLE INVERSE SHADOWING CHAIN COMPONENTS FOR GENERIC DIFFEOMORPHISMS

Title & Authors
C1-STABLE INVERSE SHADOWING CHAIN COMPONENTS FOR GENERIC DIFFEOMORPHISMS
Lee, Man-Seob;

Abstract
Let f be a diffeomorphism of a compact $\small{C^{\infty}}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $\small{C^1}$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\small{\cal{R}(f)}$ of f has $\small{C^1}$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $\small{C^1}$-generically, the chain component $\small{C_f(p)}$ of f associated to p is hyperbolic if and only if $\small{C_f(p)}$ has the $\small{C^1}$-stable inverse shadowing property.
Keywords
homoclinic class;$\small{C^1}$-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
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