Randomly connected dynamical systems - asymptotic stability

• Autorzy: Katarzyna Horbacz
• Języki publikacji: EN

Abstrakty

EN

We give sufficient conditions for asymptotic stability of a Markov operator governing the evolution of measures due to the action of randomly chosen dynamical systems. We show that the existence of an invariant measure for the transition operator implies the existence of an invariant measure for the semigroup generated by the system.

Słowa kluczowe

EN

dynamical systems; Markov operator; asymptotic stability

Kategorie tematyczne

• 47A35: Ergodic theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 68
• Numer: 1
• Strony: 31-50

Daty

wydano

1998

otrzymano

1996-05-27

poprawiono

1997-07-08

Twórcy

autor

Katarzyna Horbacz

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

Bibliografia

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• [2] K. Horbacz, Dynamical systems with multiplicative perturbations: The strong convergence of measures, Ann. Polon. Math. 58 (1993), 85-93.
• [3] W. Jarczyk and A. Lasota, Invariant measures for fractals and dynamical systems, to appear.
• [4] A. Lasota, From fractals to stochastic differential equations, to appear.
• [5] A. Lasota and M. C. Mackey, Noise and statistical periodicity, Physica D 28 (1987), 143-154.
• [6] A. Lasota and M. C. Mackey, Why do cells divide?, to appear.
• [7] A. Lasota and M. C. Mackey, Chaos, Fractals and Noise - Stochastic Aspect of Dynamics, Springer, New York, 1994.
• [8] A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynamics 2 (1994), 41-77.
• [9] T. Szarek, Iterated function systems depending on previous transformation, Univ. Iagell. Acta Math., to appear.