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http://dx.doi.org/10.4134/CKMS.2009.24.1.127

C1-STABLE INVERSE SHADOWING CHAIN COMPONENTS FOR GENERIC DIFFEOMORPHISMS  

Lee, Man-Seob (DEPARTMENT OF MATHEMATICS MOKWON UNIVERSITY)
Publication Information
Communications of the Korean Mathematical Society / v.24, no.1, 2009 , pp. 127-144 More about this Journal
Abstract
Let f be a diffeomorphism of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper we introduce the notion of $C^1$-stable inverse shadowing for a closed f-invariant set, and prove that (i) the chain recurrent set $\cal{R}(f)$ of f has $C^1$-stable inverse shadowing property if and only if f satisfies both Axiom A and no-cycle condition, (ii) $C^1$-generically, the chain component $C_f(p)$ of f associated to p is hyperbolic if and only if $C_f(p)$ has the $C^1$-stable inverse shadowing property.
Keywords
homoclinic class; $C^1$-stable inverse shadowing; residual; generic; chain recurrent; chain component; hyperbolic; axiom A;
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