본문 바로가기
KERD
논문KCI 등재

Hyperbolicity of chain transitive sets with limit shadowing

이승희|Khosro Tajbakhsh|Abbas Fakhari
대한수학회 (The Korean Mathematical Society)|2014.09|대한수학회보 (Bulletin of the KMS)|제51권 제5호|pp. 1259-1267

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

mirror symmetrynoncommutative complex torusKronecker foliation
주제분류수학

초록

In this paper we show that any chain transitive set of a diffeomorphism on a compact C∞-manifold which is C1-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a C1-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.

Abstract

In this paper we show that any chain transitive set of a diffeomorphism on a compact C∞-manifold which is C1-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a C1-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.

참고문헌 (15)

  1. F. Abdenur, "Nonuniform hyperbolicity for C1-generic diffeomorphisms", Israel J. Math, 183, pp.1~60 (2011)
  2. F. Abdenur, "Pseudo-orbit shadowing in the C1 topology", Discrete Contin. Dyn. Syst, 17(2), pp.223~245 (2007)
  3. C. Bonatti, "Dynamics beyond uniform hyperbolicity, A global geometric and probabilistic perspective, Encyclopedia of Mathematical Sciences" (2005), Springer-verlag
  4. C. Bonattio, "On the hyperoblicity of homoclinic classes", Discrete Contin. Dyn. Syst, 25(4), pp.1143~1162 (2009)
  5. S. Crovisier, "Periodic orbits and chain transitive sets of C1-diffeomorphisms", Publ. Math. Inst. Hautes ´Etudes Sci, 104, pp.87~141 (2006)
  6. A. Fakhari, "Diffeomorphisms with L p-shadowing property", Acta Math. Sin. (Engl. Ser.), 27(1), pp.19~28 (2011)
  7. J. Franks, "Necessary conditions for stability of diffeomorphisms", Trans. Amer. Math. Soc, 158, pp.301~308 (1971)
  8. K. Lee, "Hyperbolic sets with the strong limit shadowing property", J. Inequal. Appl, 6(5), pp.507~517 (2001)
  9. K. Lee, "C1-stable shadowing diffeomorphism", Discrete Contin. Dyn. Syst, 22(3), pp.683~697 (2008)
  10. 이건희, "SHADOWABLE CHAIN TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS", 대한수학회보, 49(2), pp.263~270 (2012), 대한수학회
  11. R. Ma˜n´e, "An ergodic closing lemma", Ann. of Math, 16(3), pp.503~540 (1982)
  12. R. Ma˜n´e, "A proof of the C1 stability conjecture", Inst. Hautes ´Etudes Sci. Publ. Math, 66, pp.161~210 (1988)
  13. S. Yu. Pilyugin, "Pilyugin, Shadowing in Dynamical Systems", Lecture Notes in Math, 1706 (1999), Spinger-Verlag
  14. S. Yu. Pilyugin, "Sets of dynamical systems with various limit shadowing properties", J. Dynam. Differential Equations, 19(3), pp.747~775 (2007)
  15. K. Sakai, "C1-stably shadowable chain components", Ergodic Theory Dyanam. Systems, 28(3), pp.987~1029 (2008)

관련 논문AI추천

SHADOWABLE CHAIN TRANSITIVE SETS OF C1-GENERIC DIFFEOMORPHISMS이건희, Xiao Wen대한수학회 · 대한수학회보2012 · 제49권 제2호LIMIT WEAK SHADOWABLE TRANSITIVE SETS OF C¹-GENERIC DIFFEOMORPHISMS이만섭, Gang Lu대한수학회 · 대한수학회논문집2012 · 제27권 제3호C^1-stable inverse shadowing chain components for generic diffeomorphismsManseob Lee대한수학회 · 대한수학회논문집2009 · 제24권 제1호Shadowable chain components and hyperbolicity박준미, 이만섭, 이승희대한수학회 · 대한수학회보2015 · 제52권 제1호Generic diffeomorphisms with robustly transitive sets이건희, 이만섭, 이승희대한수학회 · 대한수학회논문집2013 · 제28권 제3호Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems이만섭대한수학회 · 대한수학회지2021 · 제58권 제5호

이 간행물의 다른 논문 (23건)

Global weak Morrey estimates for some Ultraparabolic operators of Kolmogorov-Fokker-Planck typeMaochun Zhu, Xiaojing Feng, Pengcheng Niupp. 1241-1257Structural stability results for the thermoelasticity of type IIIYan Liupp. 1269-1279On the transcendental entire solutions of a class of differential equationsChungchun Yang, Weiran Lu, Qiuying Lipp. 1281-1289Value distribution of difference operator on meromorphic functionsLian-Zhong Yang, Jie Dingpp. 1291-1297UNIFORM ATTRACTORS FOR NON-AUTONOMOUS NONCLASSICAL DIFFUSION EQUATIONS ON RNCung The Anh, Nguyen Duong Toanpp. 1299-1324
원문 보기