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Funktsional. Anal. i Prilozhen., 1999, Volume 33, Issue 2, Pages 16–30 (Mi faa351)  

This article is cited in 36 scientific papers (total in 36 papers)

Certain New Robust Properties of Invariant Sets and Attractors of Dynamical Systems

A. S. Gorodetskia, Yu. S. Ilyashenkobac

a Independent University of Moscow
b Steklov Mathematical Institute, Russian Academy of Sciences
c M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics


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English version:
Functional Analysis and Its Applications, 1999, 33:2, 95–105

Bibliographic databases:

UDC: 517.938
Received: 28.12.1998

Citation: A. S. Gorodetski, Yu. S. Ilyashenko, “Certain New Robust Properties of Invariant Sets and Attractors of Dynamical Systems”, Funktsional. Anal. i Prilozhen., 33:2 (1999), 16–30; Funct. Anal. Appl., 33:2 (1999), 95–105

Citation in format AMSBIB
\by A.~S.~Gorodetski, Yu.~S.~Ilyashenko
\paper Certain New Robust Properties of Invariant Sets and Attractors of Dynamical Systems
\jour Funktsional. Anal. i Prilozhen.
\yr 1999
\vol 33
\issue 2
\pages 16--30
\jour Funct. Anal. Appl.
\yr 1999
\vol 33
\issue 2
\pages 95--105

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    This publication is cited in the following articles:
    1. A. S. Gorodetski, Yu. S. Ilyashenko, “Certain Properties of Skew Products over a Horseshoe and a Solenoid”, Proc. Steklov Inst. Math., 231 (2000), 90–112  mathnet  mathscinet  zmath
    2. R. I. Grigorchuk, “An Ergodic Theorem for the Action of a Free Semigroup”, Proc. Steklov Inst. Math., 231 (2000), 113–127  mathnet  mathscinet  zmath
    3. V. A. Kleptsyn, M. B. Nalsky, “Contraction of Orbits in Random Dynamical Systems on the Circle”, Funct. Anal. Appl., 38:4 (2004), 267–282  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Ilyashenko Y., “Selected topics in differential equations with real and complex time”, Normal Forms, Bifurcations and Finiteness Problems in Differential Equations, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 137, 2004, 317–354  crossref  mathscinet  isi
    5. A. S. Gorodetski, Yu. S. Ilyashenko, V. A. Kleptsyn, M. B. Nalsky, “Nonremovable Zero Lyapunov Exponents”, Funct. Anal. Appl., 39:1 (2005), 21–30  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Gonchenko, SV, “Three-dimensional Henon-like maps and wild Lorenz-like attractors”, International Journal of Bifurcation and Chaos, 15:11 (2005), 3493  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. A. S. Gorodetski, “The regularity of central leaves of partially hyperbolic sets and its applications”, Izv. Math., 70:6 (2006), 1093–1116  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. V. A. Kleptsyn, M. B. Nalsky, “Stability of Existence of Nonhyperbolic Measures for $C^1$-Diffeomorphisms”, Funct. Anal. Appl., 41:4 (2007), 271–283  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Diaz, LJ, “Non-hyperbolic ergodic measures for non-hyperbolic homoclinic classes”, Ergodic Theory and Dynamical Systems, 29 (2009), 1479  crossref  mathscinet  zmath  isi  scopus
    10. Bonatti, C, “Non-hyperbolic ergodic measures with large support”, Nonlinearity, 23:3 (2010), 687  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    11. A. V. Osipov, “Nondensity of the orbital shadowing property in $C^1$-topology”, St. Petersburg Math. J., 22:2 (2011), 267–292  mathnet  crossref  mathscinet  zmath  isi
    12. Ilyashenko Yu., “Thick attractors of step skew products”, Regular & Chaotic Dynamics, 15:2–3 (2010), 328–334  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Ilyashenko Yu., Negut A., “Invisible parts of attractors”, Nonlinearity, 23:5 (2010), 1199–1219  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    14. Ilyashenko Yu., “Thick attractors of boundary preserving diffeomorphisms”, Indag Math (N S ), 22:3–4 (2011), 257–314  crossref  mathscinet  zmath  isi  scopus
    15. V. A. Kleptsyn, P. S. Saltykov, “On $C^2$-stable effects of intermingled basins of attractors in classes of boundary-preserving maps”, Trans. Moscow Math. Soc., 72 (2011), 193–217  mathnet  crossref  zmath  elib
    16. Ghane F.H., Nazari M., Saleh M., Shabani Z., “Attractors and their Invisible Parts for Skew Products with High Dimensional Fiber”, Int. J. Bifurcation Chaos, 22:8 (2012), 1250182  crossref  mathscinet  zmath  isi  elib  scopus
    17. Ilyashenko Yu. Negut A., “Holder Properties of Perturbed Skew Products and Fubini Regained”, Nonlinearity, 25:8 (2012), 2377–2399  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    18. Diaz L.J., Gelfert K., “Porcupine-Like Horseshoes: Transitivity, Lyapunov Spectrum, and Phase Transitions”, Fundam. Math., 216:1 (2012), 55–100  crossref  mathscinet  zmath  isi  elib  scopus
    19. Ghane F.H., Nazari M., Saleh M., Shabani Z., “Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber”, Abstract Appl. Anal., 2013, 539736  crossref  mathscinet  zmath  isi  scopus
    20. Gonchenko S.V. Gonchenko A.S. Ovsyannikov I.I. Turaev D.V., “Examples of Lorenz-Like Attractors in Henon-Like Maps”, Math. Model. Nat. Phenom., 8:5 (2013), 48–70  crossref  mathscinet  zmath  isi  scopus
    21. Diaz L.J. Gelfert K., “Porcupine-Like Horseshoes: Topological and Ergodic Aspects”, Progress and Challenges in Dynamical Systems, Springer Proceedings in Mathematics & Statistics, 54, ed. Ibanez S. DelRio J. Pumarino A. Rodriguez J., Springer-Verlag Berlin, 2013, 199–219  crossref  mathscinet  zmath  isi  scopus
    22. Tatiana Golenishcheva-Kutuzova, Anton Gorodetski, Victor Kleptsyn, Denis Volk, “Translation numbers define generators of $F_k^+\to\mathrm{Homeo}_+(\mathbb S^1)$”, Mosc. Math. J., 14:2 (2014), 291–308  mathnet  mathscinet
    23. Barrientos P.G., Fakhari A., Sarizadeh A., “Density of Fiberwise Orbits in Minimal Iterated Function Systems on the Circle”, Discret. Contin. Dyn. Syst., 34:9 (2014), 3341–3352  crossref  mathscinet  zmath  isi  elib  scopus
    24. Barrientos P.G., Raibekas A., “Dynamics of Iterated Function Systems on the Circle Close To Rotations”, Ergod. Theory Dyn. Syst., 35:5 (2015), 1345–1368  crossref  mathscinet  zmath  isi  scopus
    25. Ilyashenko Yu., Romaskevich O., “Sternberg Linearization Theorem for Skew Products”, J. Dyn. Control Syst., 22:3 (2016), 595–614  crossref  mathscinet  zmath  isi  elib  scopus
    26. Gharaei M., Homburg A.J., “Random interval diffeomorphisms”, Discret. Contin. Dyn. Syst.-Ser. S, 10:2 (2017), 241–272  crossref  mathscinet  zmath  isi  scopus
    27. A. V. Okunev, I. S. Shilin, “On the attractors of step skew products over the Bernoulli shift”, Proc. Steklov Inst. Math., 297 (2017), 235–253  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    28. L. J. Díaz, K. Gelfert, M. Rams, “Topological and ergodic aspects of partially hyperbolic diffeomorphisms and nonhyperbolic step skew products”, Proc. Steklov Inst. Math., 297 (2017), 98–115  mathnet  crossref  crossref  mathscinet  isi  elib
    29. Das S., Yorke J.A., “Multichaos From Quasiperiodicity”, SIAM J. Appl. Dyn. Syst., 16:4 (2017), 2196–2212  crossref  mathscinet  zmath  isi  scopus
    30. Gorodetski A., Pesin Ya., “Path Connectedness and Entropy Density of the Space of Hyperbolic Ergodic Measures”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, eds. Katok A., Pesin Y., Hertz F., Amer Mathematical Soc, 2017, 111–121  crossref  mathscinet  zmath  isi
    31. Ilyashenko Yu., Shilin I., “Attractors and Skew Products”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, eds. Katok A., Pesin Y., Hertz F., Amer Mathematical Soc, 2017, 155–175  crossref  mathscinet  zmath  isi  scopus
    32. Abbasi N., Gharaei M., Homburg A.J., “Iterated Function Systems of Logistic Maps: Synchronization and Intermittency”, Nonlinearity, 31:8 (2018), 3880–3913  crossref  mathscinet  zmath  isi  scopus
    33. Diaz L.J., Gelfert K., Rams M., “Entropy Spectrum of Lyapunov Exponents For Nonhyperbolic Step Skew-Products and Elliptic Cocycles”, Commun. Math. Phys., 367:2 (2019), 351–416  crossref  mathscinet  zmath  isi  scopus
    34. Zaj M., Ghane F.H., “Non Hyperbolic Solenoidal Thick Bony Attractors”, Qual. Theor. Dyn. Syst., 18:1 (2019), 35–55  crossref  mathscinet  isi  scopus
    35. Diaz L.J., Gelfert K., Santiago B., “Weak and Entropy Approximation of Nonhyperbolic Measures: a Geometrical Approach”, Math. Proc. Camb. Philos. Soc., 169:3 (2020), 507–545  crossref  isi
    36. Gorodetski A. Kleptsyn V., “Parametric Furstenberg Theorem on Random Products of Sl(2, R) Matrices”, Adv. Math., 378 (2021), 107522  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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