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 MIAN:
Year:
Volume:
Issue:
Page:
Find






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


Tr. Mat. Inst. Steklova, 2011, Volume 273, Pages 28–29 (Mi tm3289)  

This article is cited in 2 scientific papers (total in 3 papers)

Local maximality of hyperbolic sets

D. V. Anosov

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: Two properties of a hyperbolic set $F$ are discussed: its local maximality and the property that, in any neighborhood $U\supset F$, there exists a locally maximal set $F'$ that contains $F$ (we suggest calling the latter property local premaximality). Although both these properties of the set $F$ are related to the behavior of trajectories outside $F$, it turns out that, in the class of hyperbolic sets, the presence or absence of these properties is determined by the interior dynamics on $F$.

Full text: PDF file (92 kB)
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2011, 273, 23–24

Bibliographic databases:

UDC: 517.938
Received in December 2009

Citation: D. V. Anosov, “Local maximality of hyperbolic sets”, Modern problems of mathematics, Collected papers. In honor of the 75th anniversary of the Institute, Tr. Mat. Inst. Steklova, 273, MAIK Nauka/Interperiodica, Moscow, 2011, 28–29; Proc. Steklov Inst. Math., 273 (2011), 23–24

Citation in format AMSBIB
\Bibitem{Ano11}
\by D.~V.~Anosov
\paper Local maximality of hyperbolic sets
\inbook Modern problems of mathematics
\bookinfo Collected papers. In honor of the 75th anniversary of the Institute
\serial Tr. Mat. Inst. Steklova
\yr 2011
\vol 273
\pages 28--29
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3289}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2893540}
\zmath{https://zbmath.org/?q=an:1228.37026}
\elib{http://elibrary.ru/item.asp?id=16456340}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2011
\vol 273
\pages 23--24
\crossref{https://doi.org/10.1134/S008154381104002X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000295982500002}


Linking options:
  • http://mi.mathnet.ru/eng/tm3289
  • http://mi.mathnet.ru/eng/tm/v273/p28

    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. D. V. Anosov, “On trajectories entirely situated near a hyperbolic set”, Journal of Mathematical Sciences, 201:5 (2014), 553–565  mathnet  crossref  mathscinet
    2. S. M. Aseev, V. M. Buchstaber, R. I. Grigorchuk, V. Z. Grines, B. M. Gurevich, A. A. Davydov, A. Yu. Zhirov, E. V. Zhuzhoma, M. I. Zelikin, A. B. Katok, A. V. Klimenko, V. V. Kozlov, V. P. Leksin, M. I. Monastyrskii, A. I. Neishtadt, S. P. Novikov, E. A. Sataev, Ya. G. Sinai, A. M. Stepin, “Dmitrii Viktorovich Anosov (obituary)”, Russian Math. Surveys, 70:2 (2015), 369–381  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. Fisher T., Petty T., Tikhomirov S., “Nonlocally Maximal and Premaximal Hyperbolic Sets”, 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, 83–99  crossref  mathscinet  zmath  isi
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:226
    Full text:30
    References:38

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020