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In this paper we prove that $C^1$-generically, if a diffeomorphism f on a closed $C^{\infty}$ manifold M satisfies weak specification on a locally maximal set ${\Lambda}{\subset}M$ then ${\Lambda}$ is hyperbolic for f. As a corollary we obtain that $C^1$-generically, every diffeomorphism with weak specification is Anosov.
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참고문헌 (13)
참고문헌 신청
F. Abdenur / 2007 / Pseudo-orbit shadowing in the C1 topology / Disc. Contin. Dynam. Syst 17:223~245
N. Aoki / 1982 / Solenoidal automorphisms and spec-ification / Monatshefte fÄur Mathematik 93:79~110
R. Bowen / 1971 / Periodic points and measures for Axiom A diffeomorphisms / Trans. Amer. Math. Soc 154:377~397
S. Crovisier / 2006 / Periodic orbits and chain-transitive sets of C1-diffeomorphisms / Publ. Math. IHES 104:87~141
M. Denker / 1976 / Ergodic Theory On Compact spaces / Lecture Note in Math 527
N. Aoki / 1982 / Solenoidal automorphisms and spec-ification / Monatshefte fÄur Mathematik 93:79~110
R. Bowen / 1971 / Periodic points and measures for Axiom A diffeomorphisms / Trans. Amer. Math. Soc 154:377~397
S. Crovisier / 2006 / Periodic orbits and chain-transitive sets of C1-diffeomorphisms / Publ. Math. IHES 104:87~141
M. Denker / 1976 / Ergodic Theory On Compact spaces / Lecture Note in Math 527
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