Regular and Chaotic Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regul. Chaotic Dyn., 2010, Volume 15, Issue 2-3, Pages 328–334 (Mi rcd498)  

This article is cited in 8 scientific papers (total in 8 papers)

On the 75th birthday of Professor L.P. Shilnikov

Thick attractors of step skew products

Yu. Ilyashenkoab

a V.A. Steklov Mathematical Institute, RAS, Gubkina str. 8, Moscow, 119991 Russia
b Cornell University, 310 Malott Hall, Ithaca, NY 14853-4201, USA

Abstract: A diffeomorphism is said to have a thick attractor provided that its Milnor attractor has positive but not full Lebesgue measure. We prove that there exists an open set in the space of boundary preserving step skew products with a fiber [0,1], such that any map in this set has a thick attractor.

Keywords: Milnor attractors, thick attractors, ergodicity

DOI: https://doi.org/10.1134/S1560354710020188


Bibliographic databases:

MSC: 37Cxx
Received: 16.11.2009
Accepted:04.12.2009
Language:

Citation: Yu. Ilyashenko, “Thick attractors of step skew products”, Regul. Chaotic Dyn., 15:2-3 (2010), 328–334

Citation in format AMSBIB
\Bibitem{Ily10}
\by Yu. Ilyashenko
\paper Thick attractors of step skew products
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 328--334
\mathnet{http://mi.mathnet.ru/rcd498}
\crossref{https://doi.org/10.1134/S1560354710020188}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2644340}
\zmath{https://zbmath.org/?q=an:1225.37033}


Linking options:
  • http://mi.mathnet.ru/eng/rcd498
  • http://mi.mathnet.ru/eng/rcd/v15/i2/p328

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Baranski K., Spiewak A., “Singular Stationary Measures For Random Piecewise Affine Interval Homeomorphisms”, J. Dyn. Differ. Equ.  crossref  isi  scopus
    2. V. Kleptsyn, D. Volk, “Physical measures for nonlinear random walks on interval”, Mosc. Math. J., 14:2 (2014), 339–365  mathnet  crossref  mathscinet
    3. 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
    4. 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
    5. Zaj M., Ghane F.H., “Non Hyperbolic Solenoidal Thick Bony Attractors”, Qual. Theor. Dyn. Syst., 18:1 (2019), 35–55  crossref  mathscinet  zmath  isi  scopus
    6. Gelfert K., Oliveira D., “Invariant Multi-Graphs in Step Skew-Products”, Dynam. Syst., 35:1 (2020), 1–28  crossref  mathscinet  zmath  isi  scopus
    7. Czernous W., Szarek T., “Generic Invariant Measures For Iterated Systems of Interval Homeomorphisms”, Arch. Math., 114:4 (2020), 445–455  crossref  mathscinet  zmath  isi  scopus
    8. Barrientos P.G., Fakhari A., “Ergodicity of Non-Autonomous Discrete Systems With Non-Uniform Expansion”, Discrete Contin. Dyn. Syst.-Ser. B, 25:4 (2020), 1361–1382  crossref  mathscinet  zmath  isi  scopus
  • Number of views:
    This page:25

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021