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1999 | 47 | 1 | 173-192
Tytuł artykułu

Construction of attractors and filtrations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper is a study of the global structure of the attractors of a dynamical system. The dynamical system is associated with an oriented graph called a Symbolic Image of the system. The symbolic image can be considered as a finite discrete approximation of the dynamical system flow. Investigation of the symbolic image provides an opportunity to localize the attractors of the system and to estimate their domains of attraction. A special sequence of symbolic images is considered in order to obtain precise knowledge about the global structure of the attractors and to get filtrations of the system.
Słowa kluczowe
Rocznik
Tom
47
Numer
1
Strony
173-192
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Laboratory of Nonlinear Analysis and Mathematical Modelling, St. Petersburg State Technical University, St. Petersburg 195251, Russia
Bibliografia
  • [1] V. M. Alekseev, Symbolic Dynamics, 11th Mathematical School, Kiev, 1976 (in Russian).
  • [2] N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, N.Y., Springer, 1970.
  • [3] R. Bowen, Symbolic Dynamics, Amer. Math. Soc., Providence, R.I., vol. 8, 1982.
  • [4] I. U. Bronshtein, Nonautonomous dynamical systems, Kishinev, Shtinitsa, 1984 (in Russian).
  • [5] C. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series, 38, Amer. Math. Soc., Providence, 1978.
  • [6] P. Hartman, Ordinary Differential Equations, N.Y., 1964.
  • [7] C. S. Hsu, Cell-to-Cell Mappings, Springer-Verlag, N.Y., 1987.
  • [8] M. Hurley, Chain recurrence and attraction in non-compact spaces, Ergodic Theory and Dynamical Systems 11 (1991), 709-729.
  • [9] Z. Nitecki, Differentiable Dynamics, London, 1971.
  • [10] Z. Nitecki and M. Shub, Filtrations, decompositions, and explosions, Amer. J. Math. 97 (1975), 1029-1047.
  • [11] G. S. Osipenko, On a symbolic image of dynamical system, in: Boundary value problems, Perm, 1983, 101-105 (in Russian).
  • [12] G. S. Osipenko, Verification of the transversality condition by the symbolic-dynamical methods, Differential Equations 26, 1126-1132; translated from Differentsial'nye Uravneniya 26 (1990), 1528-1536.
  • [13] G. S. Osipenko, The periodic points and symbolic dynamics, in: Seminar on Dynamical Systems, Birkhäuser Verlag, Basel, 1993, 261-267.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv47i1p173bwm
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