Poincaré's recurrence theorem for set-valued dynamical systems

• Autorzy: Jean-Pierre Aubin , Hélène Frankowska , Andrzej Lasota
• Języki publikacji: EN

Abstrakty

EN

 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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 54
• Numer: 1
• Strony: 85-91

Daty

wydano

1991

otrzymano

1990-03-25

Twórcy

autor

Jean-Pierre Aubin

• [13] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York 1964. Ceremade, Université de Paris-Dauphine, 75775 Paris Cedex 16, France

autor

Hélène Frankowska

• Paris

autor

Andrzej Lasota

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

• [1] J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis, Wiley-Interscience, 1984.
• [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.
• [4] N. Dunford and J. T. Schwartz, Linear Operators I, Wiley, New York 1957.
• [5] K. Fan, Extension of two fixed-point theorems of F. E. Browder, Math. Z. 112 (1969), 234-240.
• [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.
• [8] A. Lasota and M. C. Mackey, Globally asymptotic properties of proliferating cell populations, J. Math. Biol. 19 (1984), 43-62.
• [9] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, 1985.
• [10] A. Lasota and G. Pianigiani, Invariant measures on topological spaces. Boll. Un. Mat. Ital. (5) 14B (1977), 592-603.
• [11] A. Lasota, Invariant measures and a linear model of turbulence, Rend. Sem. Mat. Univ. Padova 61 (1979), 39-48.
• [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.