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Topological aspects of dynamical systems on manifolds

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Abstract

Necessary and sufficient conditions are presented for the existence of dynamical systems on manifolds, for which the set of nonwandering points consists of a disconnected union of 2-dimensional tori with a hyperbolic structure.

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References

  1. A. T. Fomenko and V. V. Sharko, “Exact round Morse functions, inequalities of Morse type and integrals of Hamiltonian systems,”Springer Lecture Notes in Math.,1453, 51–67 (1990).

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  2. J. Palis and W. de Melo,Geometric Theory of Dynamical Systems. An Introduction, Springer, Berlin. (1982).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev

    V. V. Sharko

Authors
  1. V. V. Sharko
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 876–878, June, 1993.

This paper was supported by the Foundation of Fundamental Researches of the Ukrainian State Committee for Science and Technology.

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Sharko, V.V. Topological aspects of dynamical systems on manifolds. Ukr Math J 45, 970–972 (1993). https://doi.org/10.1007/BF01061449

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  • DOI: https://doi.org/10.1007/BF01061449

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