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Functional Analysis and Its Applications

, Volume 33, Issue 2, pp 95–105 | Cite as

Certain new robust properties of invariant sets and attractors of dynamical systems

  • A. S. Gorodetski
  • Yu. S. Ilyashenko
Article

Keywords

Periodic Point Invariant Subset Bernoulli Shift Random Dynamical System Topological Conjugacy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. Arnold, “Random dynamical systems,” In: Lect. Notes Math., Vol. 1609, 1995, pp. 1–43.Google Scholar
  2. 2.
    G. Ch. Yuan and J. A. Yorke, “An open set of maps for which every point is absolutely nonshadowable,” Proc. Amer. Math. Soc. (to appear).Google Scholar
  3. 3.
    M. Shub, “Topologically transitive diffeomorphisms onT 4,” In: Lect. Notes Math., Vol. 206, 1971, p. 39.Google Scholar
  4. 4.
    R. Mané, “Contributions to the stability conjecture,” Topology,17, 383–396 (1978).zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    C. Bonatti and L. J. Diaz, “Persistent nonhyperbolic transitive diffeomorphisms,” Ann. Math. (2),143, No. 2, 357–396 (1996).zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    L. J. Diaz, E. Pujals, and R. Ures, Normal Hyperbolicity and Robust Transitivity, Preprint PUC-Rio, 1997.Google Scholar
  7. 7.
    C. Bonatti and M. Viana, SRB Measures for Partially Hyperbolic Systems Whose Central Direction is Mostly Contracting, Preprint IMPA, 1997.Google Scholar
  8. 8.
    M. Viana, Dynamics: A Probabilistic and Geometric Perspective. Volume, I, ICM-98, Berlin, 1998.Google Scholar
  9. 9.
    E. J. Kostelich, Ittai Kan, C. Grebogi, E. Ott, and J. Yorke, “Unstable dimension variability: A source of nonhyperbolicity in chaotic systems,” Phys. D,109, 81–90 (1997).zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    S. Dawson, C. Grebogi, T. Sauer, and J. Yorke, “Obstructions to shadowing when a Lyapunov exponent fluctuates about zero,” Phys. Rev. Lett.,73, No. 14, 1927–1930 (1994).CrossRefGoogle Scholar
  11. 11.
    M.Hirsh, C. Pugh, and M. Shub, “Invariant manifolds,” Lect. Notes Math., Vol. 583, 1977.Google Scholar
  12. 12.
    A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1995.Google Scholar
  13. 13.
    V. Nitica and A. Török, “Cohomology of dynamical systems and rigidity of partially hyperbolic actions of higher-rank lattices,” Duke Math. J.,79, No. 3, 751–810 (1995).zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    Yu. Ilyashenko and W. Li, Nonlocal Bifurcations, Amer. Math. Soc., Providence, Rhode Island, 1998.zbMATHGoogle Scholar
  15. 15.
    M. Grayson, C. Pugh, and M. Shub, “Stably ergodic diffeomorphisms,” Ann. Math. (2)140, No. 2, 295–329 (1994).zbMATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    M. Field and W. Parry, “Stable ergodicity of skew extensions by compact Lie groups,” Topology,38, No. 1, 167–187 (1999).zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1999

Authors and Affiliations

  • A. S. Gorodetski
  • Yu. S. Ilyashenko

There are no affiliations available

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