Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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QUASI-ANOSOV DIFFEOMORPHISMS AND VARIOUS SHADOWING PROPERTIES

  • Lee, Manseob (Department of Mathematics Mokwon University)
  • Received : 2016.09.09
  • Accepted : 2016.11.07
  • Published : 2016.11.15
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Abstract

In this paper, we show that if a quasi-Anosov diffeomorphism has the various types of shadowing property then it is Anosov.

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References

  1. M. L. Blank, Metric properties of ${\epsilon}$-trajectories of dynamical systems with stochastic behaviour, Ergod. Th. Dynam. Syst. 8 (1988), 365-378.
  2. A. Fakhari and F. H. Ghane, On shadowing: ordinary and ergodic, J. Math. Anal. Appl. 364 (2010), 151-155. https://doi.org/10.1016/j.jmaa.2009.11.004
  3. J. Franks and C. Robinson, A quasi-Anosov diffeomorphism that is not Anosov, Tran. Amer. Math. Soc. 223 (1976), 267-278. https://doi.org/10.1090/S0002-9947-1976-0423420-9
  4. J. Franks and J. Selgrade, Hyperbolicity and chain recurrence, J. Diff. Eqaut. 26 (1977), 27-36. https://doi.org/10.1016/0022-0396(77)90096-1
  5. R. Gu, The asymptotic average shadowing property and transitivity, Nonlinear Anal. 67 (2007), 1680-1689. https://doi.org/10.1016/j.na.2006.07.040
  6. M. Lee and J. Park, Diffeomorphisms with Average and Asymptotic Average Shadowing, Dynam. Contin. Discrete and Impulsive Systems, Series A: Math. Anal. 23 (2016) 285-294.
  7. M. Lee, Robustly chain transitive diffeomorphisms, J. Inequal. Appl. 2015, 2015:230, 1-6.
  8. R. Mane, Quasi-Anosov diffeomorphisms and hyperbolic manifolds, Trans. Amer. Math. Soc. 38 (1980), 192-209.
  9. J. Palis, On the $C^1$-stability conjecture, IHES Publ. Math. 66 (1988), 211-215.
  10. J. Park and Y. Zhang, Average shadowing properties on compact metric spaces, Commun. Korean Math. Soc. 21 (2006), 355-361. https://doi.org/10.4134/CKMS.2006.21.2.355
  11. K. Sakai, Quasi-Anosov diffeomorphisms and pseudo-orbit tracing property, Nagoya Math. J. 111 (1988), 111-114. https://doi.org/10.1017/S0027763000001021