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CMFD, 2012, Volume 45, Pages 5–17 (Mi cmfd209)  

This article is cited in 1 scientific paper (total in 2 paper)

On trajectories entirely situated near a hyperbolic set

D. V. Anosovab

a Lomonosov Moscow State University, Moscow, Russia
b Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

Abstract: Let $I_1$ be a set of points such that their trajectories under a diffeomorphism $f_1$ are entirely close enough to a hyperbolic set $F_1$ of this diffeomorphism. Then it is proved that the structure of $I_1$ and restriction $f_1|_{I_1}$ (“motion in $I_1$”) are essentially defined (up to an equivariant homeomorphism) by “internal dynamics” in $F_1$, i.e., by the restriction $f_1|_{F_1}$. (In more detail: the equivariant homeomorphism $g_1$ of the set $F_1$ on the hyperbolic set $F_2$ of the second diffeomorphism $f_2$ (probably, acting on another manifold $M_2$) is extendable to an equivariant homeomorphic embedding $I_1\to M_2$. The image of the imbedding contains all the trajectories $f_2$ close enough to $F_2$.)

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00384
Ministry of Education and Science of the Russian Federation НШ-8508.2010.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations


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English version:
Journal of Mathematical Sciences, 2014, 201:5, 553–565

Bibliographic databases:

UDC: 517.938

Citation: D. V. Anosov, “On trajectories entirely situated near a hyperbolic set”, Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2011). Part 1, CMFD, 45, PFUR, M., 2012, 5–17; Journal of Mathematical Sciences, 201:5 (2014), 553–565

Citation in format AMSBIB
\Bibitem{Ano12}
\by D.~V.~Anosov
\paper On trajectories entirely situated near a~hyperbolic set
\inbook Proceedings of the Sixth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2011). Part~1
\serial CMFD
\yr 2012
\vol 45
\pages 5--17
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd209}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3087049}
\transl
\jour Journal of Mathematical Sciences
\yr 2014
\vol 201
\issue 5
\pages 553--565
\crossref{https://doi.org/10.1007/s10958-014-2011-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84905879736}


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    This publication is cited in the following articles:
    1. 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
    2. T. Fisher, T. Petty, S. Tikhomirov, “Nonlocally maximal and premaximal hyperbolic sets”, Modern Theory of Dynamical Systems: a Tribute to Dmitry Victorovich Anosov, Contemporary Mathematics, 692, eds. A. Katok, Y. Pesin, F. Hertz, Amer. Math. Soc., 2017, 83–99  crossref  mathscinet  zmath  isi  scopus
  • Современная математика. Фундаментальные направления
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