# 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

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topJean-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

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

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