Poincaré's recurrence theorem for set-valued dynamical systems

Jean-Pierre Aubin; Hélène Frankowska; Andrzej Lasota

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 1, page 85-91
  • ISSN: 0066-2216

Abstract

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 Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.

How to cite

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Jean-Pierre Aubin, Hélène Frankowska, and Andrzej Lasota. "Poincaré's recurrence theorem for set-valued dynamical systems." Annales Polonici Mathematici 54.1 (1991): 85-91. <http://eudml.org/doc/263557>.

@article{Jean1991,
abstract = { Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.},
author = {Jean-Pierre Aubin, Hélène Frankowska, Andrzej Lasota},
journal = {Annales Polonici Mathematici},
keywords = {invariant measure; Poincaré’s recurrence theorem; set-valued dynamical systems},
language = {eng},
number = {1},
pages = {85-91},
title = {Poincaré's recurrence theorem for set-valued dynamical systems},
url = {http://eudml.org/doc/263557},
volume = {54},
year = {1991},
}

TY - JOUR
AU - Jean-Pierre Aubin
AU - Hélène Frankowska
AU - Andrzej Lasota
TI - Poincaré's recurrence theorem for set-valued dynamical systems
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 1
SP - 85
EP - 91
AB -  Abstract. The existence theorem of an invariant measure and Poincare's Recurrence Theorem are extended to set-valued dynamical systems with closed graph on a compact metric space.
LA - eng
KW - invariant measure; Poincaré’s recurrence theorem; set-valued dynamical systems
UR - http://eudml.org/doc/263557
ER -

References

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  1. [1] J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley-Interscience, 1984. Zbl0641.47066
  2. [2] J.-P. Aubin qnd H. Frankowska, Set-Valued Analysis (to appear). 
  3. [3] J.-P. Aubin, Mathematical Methods of Game and Economic Theory, Stud. Math. Appl. 7, North-Holland, 1979. Zbl0452.90093
  4. [4] N. Dunford and J. T. Schwartz, Linear Operators I, Wiley, New York 1957. Zbl0084.10402
  5. [5] K. Fan, Extension of two fixed-point theorems of F. E. Browder, Math. Z. 112 (1969), 234-240. Zbl0185.39503
  6. [6] K. Fan,, A minimax inequality and applications, in: Inequalities III, Shisha Ed., 1972. 
  7. [7] B. O. Koopman, Hamiltonian systems and transformations in Hilbert spaces, Proc. Nat. Acad. Sci. U.S.A. 17 (1931), 315-318. Zbl0002.05701
  8. [8] A. Lasota and M. C. Mackey, Globally asymptotic properties of proliferating cell populations, J. Math. Biol. 19 (1984), 43-62. Zbl0529.92011
  9. [9] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, 1985. Zbl0606.58002
  10. [10] A. Lasota and G. Pianigiani, Invariant measures on topological spaces. Boll. Un. Mat. Ital. (5) 14B (1977), 592-603. Zbl0372.28019
  11. [11] A. Lasota, Invariant measures and a linear model of turbulence, Rend. Sem. Mat. Univ. Padova 61 (1979), 39-48. Zbl0459.28025
  12. [12] A. Lasota, Statistical stability of deterministic systems, Lecture Notes in Math. 82, Springer, Berlin 1982, 386-419. 
  13. [13] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York 1964. Zbl0137.24201

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