Construction of attractors and filtrations

George Osipenko

Banach Center Publications (1999)

  • Volume: 47, Issue: 1, page 173-192
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Osipenko, George. "Construction of attractors and filtrations." Banach Center Publications 47.1 (1999): 173-192. <http://eudml.org/doc/208932>.

@article{Osipenko1999,
abstract = {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.},
author = {Osipenko, George},
journal = {Banach Center Publications},
keywords = {symbolic dynamics; attractors; filtration},
language = {eng},
number = {1},
pages = {173-192},
title = {Construction of attractors and filtrations},
url = {http://eudml.org/doc/208932},
volume = {47},
year = {1999},
}

TY - JOUR
AU - Osipenko, George
TI - Construction of attractors and filtrations
JO - Banach Center Publications
PY - 1999
VL - 47
IS - 1
SP - 173
EP - 192
AB - 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.
LA - eng
KW - symbolic dynamics; attractors; filtration
UR - http://eudml.org/doc/208932
ER -

References

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  1. [1] V. M. Alekseev, Symbolic Dynamics, 11th Mathematical School, Kiev, 1976 (in Russian). 
  2. [2] N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, N.Y., Springer, 1970. Zbl0213.10904
  3. [3] R. Bowen, Symbolic Dynamics, Amer. Math. Soc., Providence, R.I., vol. 8, 1982. Zbl0257.54042
  4. [4] I. U. Bronshtein, Nonautonomous dynamical systems, Kishinev, Shtinitsa, 1984 (in Russian). 
  5. [5] C. Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series, 38, Amer. Math. Soc., Providence, 1978. 
  6. [6] P. Hartman, Ordinary Differential Equations, N.Y., 1964. 
  7. [7] C. S. Hsu, Cell-to-Cell Mappings, Springer-Verlag, N.Y., 1987. 
  8. [8] M. Hurley, Chain recurrence and attraction in non-compact spaces, Ergodic Theory and Dynamical Systems 11 (1991), 709-729. Zbl0785.58033
  9. [9] Z. Nitecki, Differentiable Dynamics, London, 1971. 
  10. [10] Z. Nitecki and M. Shub, Filtrations, decompositions, and explosions, Amer. J. Math. 97 (1975), 1029-1047. Zbl0324.58015
  11. [11] G. S. Osipenko, On a symbolic image of dynamical system, in: Boundary value problems, Perm, 1983, 101-105 (in Russian). 
  12. [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. [13] G. S. Osipenko, The periodic points and symbolic dynamics, in: Seminar on Dynamical Systems, Birkhäuser Verlag, Basel, 1993, 261-267. Zbl0802.34046

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