RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2010, Volume 87, Issue 5, Pages 650–668 (Mi mz8715)  

This article is cited in 5 scientific papers (total in 6 papers)

On Certain Hyperbolic Sets

D. V. Anosov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: Two invariant sets $F$ of certain diffeomorphisms $S$ that were described by A. Fathi, S. Crovisier, and T. Fisher as examples of hyperbolic sets with the property (unexpected at that time) that, in some neighborhood of such an $F$, there is no locally maximal set containing $F$ are considered. It is proved that this property, although referring to the behavior of the orbits of $S$ near $F$, is ultimately determined in the examples mentioned above by a combination of a certain explicitly stated intrinsic property of the action of $S$ on $F$ with the hyperbolicity of $F$. (This means that if a hyperbolic set $F'$ for a diffeomorphism $S'$ is equivariantly homeomorphic to a Fathi–Crovisier or a Fisher set, then $F'$ has a neighborhood in which $S'$ has no locally maximal set containing $F'$.)

Keywords: non–locally premaximal hyperbolic set, non–locally premaximal hyperbolic set, hyperbolic set, locally maximal (premaximal) invariant set, metric space

DOI: https://doi.org/10.4213/mzm8715

Full text: PDF file (553 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2010, 87:5, 608–622

Bibliographic databases:

UDC: 517.938
Received: 11.12.2009

Citation: D. V. Anosov, “On Certain Hyperbolic Sets”, Mat. Zametki, 87:5 (2010), 650–668; Math. Notes, 87:5 (2010), 608–622

Citation in format AMSBIB
\Bibitem{Ano10}
\by D.~V.~Anosov
\paper On Certain Hyperbolic Sets
\jour Mat. Zametki
\yr 2010
\vol 87
\issue 5
\pages 650--668
\mathnet{http://mi.mathnet.ru/mz8715}
\crossref{https://doi.org/10.4213/mzm8715}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2766421}
\transl
\jour Math. Notes
\yr 2010
\vol 87
\issue 5
\pages 608--622
\crossref{https://doi.org/10.1134/S0001434610050020}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000279600700002}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77954414379}


Linking options:
  • http://mi.mathnet.ru/eng/mz8715
  • https://doi.org/10.4213/mzm8715
  • http://mi.mathnet.ru/eng/mz/v87/i5/p650

    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. Anosov D.V., “Intrinsic character of one property of hyperbolic sets”, J. Dyn. Control Syst., 16:4 (2010), 485–493  crossref  mathscinet  zmath  isi  scopus
    2. D. V. Anosov, “Local maximality of hyperbolic sets”, Proc. Steklov Inst. Math., 273 (2011), 23–24  mathnet  crossref  mathscinet  zmath  isi  elib
    3. D. V. Anosov, “On trajectories entirely situated near a hyperbolic set”, Journal of Mathematical Sciences, 201:5 (2014), 553–565  mathnet  crossref  mathscinet
    4. 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
    5. 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  scopus
    6. Da Luz A., “Hyperbolic Sets That Are Not Contained in a Locally Maximal One”, Discret. Contin. Dyn. Syst., 37:9 (2017), 4923–4941  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
    Number of views:
    This page:401
    Full text:131
    References:39
    First page:26

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