Download PDF - Randomly connected dynamical systems - asymptotic stabilityAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Randomly connected dynamical systems - asymptotic stability

Authors 1

Affiliations

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

Abstract

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.

Keywords

ENG
dynamical systems, Markov operator, asymptotic stability

Bibliography

  1. R. Fortet et B. Mourier, Convergence de la répartition empirique vers la répartition théorétique, Ann. Sci. École Norm. Sup. 70 (1953), 267-285.
  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.
Annales Polonici Mathematici
1998/68/1
Export to PBN, Opens in new tab
Pages:
31-50
Main language of publication
English
Received
1996-05-27
Accepted
1997-07-08
Published
1998
Exact and natural sciences