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Stable weak shadowable symplectomorphisms are partially hyperbolic

Mario Bessa|Sandra Vaz
대한수학회 (The Korean Mathematical Society)|2014.04|대한수학회논문집 (Communications of the KMS)|제29권 제2호|pp. 285-293

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참고문헌

키워드

partial hyperbolicityweak shadowingsymplectomorphisms
주제분류수학

초록

Let M be a closed, symplectic connected Riemannian mani- fold and f a symplectomorphism on M. We prove that if f is C1-stably weak shadowable on M, then the whole manifold M admits a partially hyperbolic splitting.

Abstract

Let M be a closed, symplectic connected Riemannian mani- fold and f a symplectomorphism on M. We prove that if f is C1-stably weak shadowable on M, then the whole manifold M admits a partially hyperbolic splitting.

참고문헌 (30)

  1. F. Abdenur, "Transitivity and topological mixing for C¹ diffeomorphisms, Essays in mathematics and its applications", pp.1~16 (2012), Springer
  2. M.-C. Arnaud, "Dynamique sympletiques generiques", Ergodic Theory Dynam. Systems, 25(5), pp.1401~1436 (2005)
  3. A. Avila, "Nonuniform center bunching and the genericity of ergodicity among C¹ partially hyperbolic symplectomorphisms", Ann. Sci. Ec. Norm. Super, 42(6), pp.931~979 (2009)
  4. Mario Bessa, "C1-STABLY SHADOWABLE CONSERVATIVE DIFFEOMORPHISMS ARE ANOSOV", 대한수학회보, 50(5), pp.1495~1499 (2013), 대한수학회
  5. M. Bessa, "weakly shadowable volume-preserving systems are volume-hyperbolic", Acta Math. Sin.(Engl. Ser.), 30(6), pp.1007~1020 (2014)
  6. M. Bessa, "A remark on the topological stability of symplectomorphisms", Appl. Math. Lett, 25(2), pp.163~165 (2012)
  7. J. Bochi, "Lyapunov exponents: How frequently are dynamical systems hyperbolic?, in Modern Dynamical Systems and Applications", pp.271~297 (2004), Cambridge Univ. Press
  8. C. Bonatti, "Dynamics beyond uniform hyperbolicity" (2005), Springer-Verlag
  9. C. Bonatti, "SRB measures for partially hyperbolic systems whose central direction is mostly contracting", Israel J. Math, 115, pp.157~193 (2000)
  10. R. Bowen, "Equilibrium states and the ergodic theory of Anosov diffeomorphisms" (1975), Springer
  11. M. Brin, "Topological transitivity of one class of dynamical systems and flows of frames on manifolds of negative curvature", Funct. Anal. Appl, 9(1), pp.8~16 (1975)
  12. R. M. Corless, "Approximate and real trajectories for generic dynamical systems", J. Math. Anal. Appl, 189(2), pp.409~423 (1995)
  13. S. Crovisier, "Periodic orbits and chain-transitive sets of C1-diffeomorphisms", Publ. Math. Inst. Hautes Etudes Sci, 104, pp.87~141 (2006)
  14. D. Dolgopyat, "Stable accessibility is C¹ dense", Asterisque, 287, pp.33~60 (2003)
  15. S. Gan, "C1-stably weakly shadowing homoclinic classes admit dominated splitting", Discrete Contin. Dyn. Syst, 27(1), pp.205~216 (2010)
  16. R. Gu, "The asymptotic average-shadowing property and transitivity for flows", Chaos Solitons Fractals, 41(5), pp.2234~2240 (2009)
  17. V. Horita, "Partial hyperbolicity for symplectic diffeomorphisms", Ann. Inst. H. Poincare Anal. Non Lineaire, 23(5), pp.641~661 (2006)
  18. M. Lee, "Volume preserving diffeomorphisms with weak and limit weak shadowing Dyn", Contin. Discrete Impuls. Syst. Ser. A Math. Anal, 20(3), pp.319~325 (2013)
  19. J. Moser, "Notes on dynamical systems" (2005), American Mathematical Society
  20. S. Newhouse, "Quasi-elliptic periodic points in conservative dynamical systems", Amer. J. Math, 99(5), pp.1061~1087 (1977)
  21. S. Yu. Pilyugin, "Shadowing in Dynamical Systems" (1999), Berlin
  22. S. Yu. Pilyugin, "Transversality properties and C1-open sets of diffeomorphisms with weak shadowing", Discrete Contin. Dyn. Syst, 16(4), pp.871~882 (2006)
  23. E. R. Pujals, "Some simple questions related to the Cr stability conjecture", Nonlinearity, 21(11), pp.233~237 (2008)
  24. C. Robinson, "Generic Properties of Conservative Systems. II", Amer. J. Math, 92(4), pp.897~906 (1970)
  25. K. Sakai, "C¹-stably shadowable chain components", Ergodic Theory Dynam. Systems, 28(3), pp.987~1029 (2008)
  26. K. Sakai, "Diffeomorphisms with weak shadowing", Fund. Math, 168(1), pp.57~75 (2001)
  27. K. Sakai, "Diffeomorphisms with the average-shadowing property on two-dimensional closed manifolds", Rocky Mountain J. Math, 30(3), pp.1129~1137 (2000)
  28. A. Tahzibi, "Stably ergodic diffeomorphisms which are not partially hyperbolic", Israel J. Math, 142, pp.315~344 (2004)
  29. D. Yang, "Stably weakly shadowing transitive sets and dominated splittings", Proc. Amer. Math. Soc, 139(8), pp.2747~2751 (2011)
  30. R. Saghin, "Partial hyperbolicity or dense elliptic periodic points for C1-generic symplectic diffeomorphisms", Trans. Amer. Math. Soc, 358(11), pp.5119~5138 (2006)

관련 논문AI추천

C1-STABLY SHADOWABLE CONSERVATIVE DIFFEOMORPHISMS ARE ANOSOVMario Bessa대한수학회 · 대한수학회보2013 · 제50권 제5호LIMIT WEAK SHADOWABLE TRANSITIVE SETS OF C¹-GENERIC DIFFEOMORPHISMS이만섭, Gang Lu대한수학회 · 대한수학회논문집2012 · 제27권 제3호SHADOWABLE 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 제5호Generic diffeomorphisms with robustly transitive sets이건희, 이만섭, 이승희대한수학회 · 대한수학회논문집2013 · 제28권 제3호Shadowable chain components and hyperbolicity박준미, 이만섭, 이승희대한수학회 · 대한수학회보2015 · 제52권 제1호

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