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

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References

  1. L. Arnold, “Random dynamical systems,” In: Lect. Notes Math., Vol. 1609, 1995, pp. 1–43.

  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).

  3. M. Shub, “Topologically transitive diffeomorphisms onT 4,” In: Lect. Notes Math., Vol. 206, 1971, p. 39.

  4. R. Mané, “Contributions to the stability conjecture,” Topology,17, 383–396 (1978).

    Article  MATH  MathSciNet  Google Scholar 

  5. C. Bonatti and L. J. Diaz, “Persistent nonhyperbolic transitive diffeomorphisms,” Ann. Math. (2),143, No. 2, 357–396 (1996).

    Article  MATH  MathSciNet  Google Scholar 

  6. L. J. Diaz, E. Pujals, and R. Ures, Normal Hyperbolicity and Robust Transitivity, Preprint PUC-Rio, 1997.

  7. C. Bonatti and M. Viana, SRB Measures for Partially Hyperbolic Systems Whose Central Direction is Mostly Contracting, Preprint IMPA, 1997.

  8. M. Viana, Dynamics: A Probabilistic and Geometric Perspective. Volume, I, ICM-98, Berlin, 1998.

  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).

    Article  MATH  MathSciNet  Google Scholar 

  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).

    Article  Google Scholar 

  11. M.Hirsh, C. Pugh, and M. Shub, “Invariant manifolds,” Lect. Notes Math., Vol. 583, 1977.

  12. A. Katok and B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, 1995.

  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).

    Article  MATH  MathSciNet  Google Scholar 

  14. Yu. Ilyashenko and W. Li, Nonlocal Bifurcations, Amer. Math. Soc., Providence, Rhode Island, 1998.

    MATH  Google Scholar 

  15. M. Grayson, C. Pugh, and M. Shub, “Stably ergodic diffeomorphisms,” Ann. Math. (2)140, No. 2, 295–329 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  16. M. Field and W. Parry, “Stable ergodicity of skew extensions by compact Lie groups,” Topology,38, No. 1, 167–187 (1999).

    Article  MATH  MathSciNet  Google Scholar 

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The authors were supported in part by grants RFBR 98-01-00455, INTAS-93-0570 ext, and CRDF RM1-229.

Independent Moscow University. Moscow State University, Independent Moscow University, V. A. Steklov Mathematical Institute of RAN, Cornell University. Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 33, No. 2, pp. 16–30, April–June, 1999.

Translated by A. S. Gorodetski

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Gorodetski, A.S., Ilyashenko, Y.S. Certain new robust properties of invariant sets and attractors of dynamical systems. Funct Anal Its Appl 33, 95–105 (1999). https://doi.org/10.1007/BF02465190

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  • DOI: https://doi.org/10.1007/BF02465190

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