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Shadowable chain components and hyperbolicity

이승희|이만섭|박준미
대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회보 (Bulletin of the KMS)|제52권 제1호|pp. 149-157

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참고문헌

키워드

hyperbolicchain componentshadowable
주제분류수학

초록

We show that $C^1$-generically, the shadowable chain component of a $C^1$-vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.

Abstract

We show that $C^1$-generically, the shadowable chain component of a $C^1$-vector field containing a hyperbolic periodic orbit is hyperbolic if it is locally maximal.

참고문헌 (11)

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  4. S. Hayashi, "Connecting invariant manifolds and the solution of the C1 stability and Ω-stability conjectures for flows", Ann. of Math, 145(1), pp.81~137 (1997)
  5. K. Lee, "Hyperbolicity of expansive homoclinic classes", ~
  6. 이건희, "ROBUSTLY SHADOWABLE CHAIN COMPONENTS OF C¹ VECTOR FIELDS", 대한수학회지, 51(1), pp.17~53 (2014), 대한수학회
  7. K. Moriyasu, "Vector fields with topological stability", Trans. Amer. Math. Soc, 353(8), pp.3391~3408 (2001)
  8. R. Ribeiro, "Hyperbolicity and types of shadowing for C1 generic vector fields", arXiv: 1305.2977v1, ~
  9. K. Sakai, "C1-stably shadowable chain components", Ergodic Theory Dynam. Systems, 28(3), pp.987~1029 (2008)
  10. L. Senos, "Generic Bowen-expansive flows", Bull. Braz. Math. Soc, 43(1), pp.59~71 (2012)
  11. L. Wen, "C1-stably shadowable chain components are hyperbolic", J. Differential Equations, 236(1), pp.340~357 (2009)

관련 논문AI추천

SHADOWABLE CHAIN TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS이건희, Xiao Wen대한수학회 · 대한수학회보2012 · 제49권 제2호Hyperbolicity of chain transitive sets with limit shadowing이승희, Abbas Fakhari, Khosro Tajbakhsh대한수학회 · 대한수학회보2014 · 제51권 제5호C^1-stable inverse shadowing chain components for generic diffeomorphismsManseob Lee대한수학회 · 대한수학회논문집2009 · 제24권 제1호ROBUSTLY SHADOWABLE CHAIN COMPONENTS OF C¹ VECTOR FIELDS이건희, Le Huy Tien, Xiao Wen대한수학회 · 대한수학회지2014 · 제51권 제1호Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems이만섭대한수학회 · 대한수학회지2021 · 제58권 제5호LIMIT WEAK SHADOWABLE TRANSITIVE SETS OF C¹-GENERIC DIFFEOMORPHISMS이만섭, Gang Lu대한수학회 · 대한수학회논문집2012 · 제27권 제3호

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