Trudy Matematicheskogo Instituta imeni V.A. Steklova
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy Mat. Inst. Steklova:
Year:
Volume:
Issue:
Page:
Find






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


Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 297, Pages 260–280
DOI: https://doi.org/10.1134/S0371968517020145
(Mi tm3804)
 

This article is cited in 3 scientific papers (total in 3 papers)

On the attractors of step skew products over the Bernoulli shift

A. V. Okuneva, I. S. Shilinb

a National Research University "Higher School of Economics", ul. Myasnitskaya 20, Moscow, 101000 Russia
b Moscow Center for Continuous Mathematical Education, Bol'shoi Vlas'evskii per. 11, Moscow, 119002 Russia
Full-text PDF (307 kB) Citations (3)
References:
Abstract: We study the statistical and Milnor attractors of step skew products over the Bernoulli shift. In the case when the fiber is a circle, we prove that for a topologically generic step skew product the statistical and Milnor attractors coincide and are Lyapunov stable. To this end we study some properties of the projection of the attractor onto the fiber, which might be of independent interest. In the case when the fiber is a segment, we give a description of the Milnor attractor as the closure of the union of graphs of finitely many almost everywhere defined functions from the base of the skew product to the fiber.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00748-а
This work was supported by the Russian Foundation for Basic Research, project no. 16-01-00748-a.
Received: February 20, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 297, Pages 235–253
DOI: https://doi.org/10.1134/S0081543817040149
Bibliographic databases:
Document Type: Article
UDC: 517.938
Language: Russian
Citation: A. V. Okunev, I. S. Shilin, “On the attractors of step skew products over the Bernoulli shift”, Order and chaos in dynamical systems, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov, Trudy Mat. Inst. Steklova, 297, MAIK Nauka/Interperiodica, Moscow, 2017, 260–280; Proc. Steklov Inst. Math., 297 (2017), 235–253
Citation in format AMSBIB
\Bibitem{OkuShi17}
\by A.~V.~Okunev, I.~S.~Shilin
\paper On the attractors of step skew products over the Bernoulli shift
\inbook Order and chaos in dynamical systems
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Dmitry Victorovich Anosov
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 297
\pages 260--280
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3804}
\crossref{https://doi.org/10.1134/S0371968517020145}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3695417}
\zmath{https://zbmath.org/?q=an:1377.37023}
\elib{https://elibrary.ru/item.asp?id=29859500}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2017
\vol 297
\pages 235--253
\crossref{https://doi.org/10.1134/S0081543817040149}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000410199700014}
\elib{https://elibrary.ru/item.asp?id=31041775}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85029154969}
Linking options:
  • https://www.mathnet.ru/eng/tm3804
  • https://doi.org/10.1134/S0371968517020145
  • https://www.mathnet.ru/eng/tm/v297/p260
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Statistics & downloads:
    Abstract page:235
    Full-text PDF :43
    References:34
    First page:10
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024