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Let f be a diffeomorphism of a
compact C^∞ 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 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.
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참고문헌 (16)
참고문헌 신청
C. Bonatti / 2004 / Recurrence et genericite / Invent. Math. 158 : 33 ~ 104
C. Robinson / 1999 / Dynamical Systems: stability, symbolic dynamics, and chaos (2-nd Ed.): Studies in Advanced Mathematics / CRC Press
F. Abdenur / 2007 / Pseodo-orbit shadowing in the C¹-topology / Discrete Contin. Dyn. Syst. 17 : 223 ~ 245
J. Franks / 1971 / Necessary conditions for stability of diffeomorphisms / Trans. Amer. Math. Soc. 158 : 301 ~ 308
J. Palis / 1993 / Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations / Cambridge Studies in Advanced Mathematics 35
C. Robinson / 1999 / Dynamical Systems: stability, symbolic dynamics, and chaos (2-nd Ed.): Studies in Advanced Mathematics / CRC Press
F. Abdenur / 2007 / Pseodo-orbit shadowing in the C¹-topology / Discrete Contin. Dyn. Syst. 17 : 223 ~ 245
J. Franks / 1971 / Necessary conditions for stability of diffeomorphisms / Trans. Amer. Math. Soc. 158 : 301 ~ 308
J. Palis / 1993 / Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations / Cambridge Studies in Advanced Mathematics 35
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