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1999 | 47 | 1 | 57-65
Tytuł artykułu

Conley index for set-valued maps: from theory to computation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recent results on the Conley index theory for discrete multi-valued dynamical systems with their consequences for the computation of the index for representable maps are recapitulated. The terminology is simplified with respect to previous presentations, some superfluous hypotheses are abandoned and some conclusions are proved in a simpler way.
Słowa kluczowe
Rocznik
Tom
47
Numer
1
Strony
57-65
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Département de mathématiques et d'informatique, Université de Sherbrooke, Sherbrooke J1K 2R1 (Qc), Canada
Bibliografia
  • [1] M. Allili and T. Kaczynski, An algorithmic approach to the construction of homomorphisms induced by maps in homology, Trans. Amer. Math. Soc., to appear.
  • [2] R. Bowen, Equilibrium States and The Ergodic Theory of Anosov Diffeomorphisms, Lecture Notes in Math. (470), Springer, 1975.
  • [3] L. Górniewicz, Homological Methods in Fixed Point Theory of Multi-Valued Maps, Dissertationes Math. (129), PWN, Warsaw, 1976.
  • [4] T. Kaczynski and M. Mrozek, Conley index for discrete multivalued dynamical systems, Topology Appl. 65 (1995), 83-96.
  • [5] T. Kaczynski and M. Mrozek, Stable index pairs for discrete dynamical systems, Canad. Math. Bull. 40 (4) (1997), 448-455.
  • [6] T. Kaczynski and M. Mrozek, Connected simple systems and the Conley functor, Topol. Meth. in Nonlin. Anal. 10 (1) (1997), 183-193.
  • [7] T. Kaczynski, M. Mrozek and M. Ślusarek, Homology computation by reduction of chain complexes, Computers & Math. Appl. 35 (4) (1998), 59-70.
  • [8] W. Kalies, K. Mischaikow and G. Watson, Cubical approximation and computation of homology, this volume.
  • [9] K. Mischaikow and M. Mrozek, Isolating neighborhoods and chaos, Japan J. Ind. and Appl. Math. 12 (1995), 205-236.
  • [10] K. Mischaikow and M. Mrozek, Chaos in the Lorenz equations: a computer assisted proof, Bull. Amer. Math. Soc. 32 (1995), 66-72.
  • [11] K. Mischaikow, M. Mrozek, J. Reiss and A. Szymczak, From time series to symbolic dynamics: an algebraic topological approach, preprint.
  • [12] M. Mrozek, Leray functor and cohomological index for discrete dynamical systems, Trans. Amer. Math. Soc. 318 (1990), 149-178.
  • [13] M. Mrozek, An algorithmic approach to the Conley index theory, preprint.
  • [14] J. W. Robbin and D. Salamon, Dynamical systems, shape theory and the Conley index, Ergodic Theory Dynamical Systems 8 (1988), 375-393.
  • [15] E. H. Spanier, Algebraic Topology, McGraw-Hill, 1966.
  • [16] A. Szymczak, A combinatorial procedure for finding isolating neighborhoods and index pairs, Proc. Royal Soc. Edinburgh Sect. A 127 (5) (1997), 1075-1088.
  • [17] A. Szymczak, The Conley index for discrete semidynamical systems, Topology Appl. 66 (3) (1995), 214-240.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv47i1p57bwm
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