대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제50권5호
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  • Pages.1495-1499
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  • 2013
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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C1-STABLY SHADOWABLE CONSERVATIVE DIFFEOMORPHISMS ARE ANOSOV

  • 투고 : 2012.01.23
  • 발행 : 2013.09.30
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초록

In this short note we prove that if a symplectomorphism $f$ is $C^1$-stably shadowable, then $f$ is Anosov. The same result is obtained for volume-preserving diffeomorphisms.

키워드

참고문헌

  1. A. Arbieto and T. Catalan, Hyperbolicity in the Volume Preserving Scenario, Ergod. Th. & Dynam. Sys. (at press) DOI: http://dx.doi.org/10.1017/etds.2012.111.
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  6. V. Horita and A. Tahzibi, Partial hyperbolicity for symplectic diffeomorphisms, Ann. Inst. H. Poincare Anal. Non Lineaire 23 (2006), no. 5, 641-661. https://doi.org/10.1016/j.anihpc.2005.06.002
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  8. J. Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286-294. https://doi.org/10.1090/S0002-9947-1965-0182927-5
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  11. S. Pilyugin, Shadowing in Dynamical Systems, Lecture Notes in Math., 1706, Springer-Verlag, Berlin, 1999.
  12. K. Sakai, $C^1$-stably shadowable chain components, Ergodic Theory Dynam. Systems 28 (2008), no. 3, 987-1029.
  13. P. Walters, On the pseudo-orbit tracing property and its relationship to stability, The structure of attractors in dynamical systems (Proc. Conf., North Dakota State Univ., Fargo, N.D., 1977), 231-244, Lecture Notes in Math., 668, Springer, Berlin, 1978.
  14. E. Zehnder, Note on smoothing symplectic and volume-preserving diffeomorphisms, Geometry and topology (Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq, Rio de Janeiro, 1976), pp. 828-854. Lecture Notes in Math., Vol. 597, Springer, Berlin, 1977.

피인용 문헌

  1. STABLE WEAK SHADOWABLE SYMPLECTOMORPHISMS ARE PARTIALLY HYPERBOLIC vol.29, pp.2, 2014, https://doi.org/10.4134/CKMS.2014.29.2.285
  2. Shadowing, expansiveness and specification for C1-conservative systems vol.35, pp.3, 2015, https://doi.org/10.1016/S0252-9602(15)30005-9
  3. Symplectic diffeomorphisms with limit shadowing vol.10, pp.02, 2017, https://doi.org/10.1142/S1793557117500681