# Randomly connected dynamical systems - asymptotic stability

Annales Polonici Mathematici (1998)

- Volume: 68, Issue: 1, page 31-50
- ISSN: 0066-2216

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topKatarzyna Horbacz. "Randomly connected dynamical systems - asymptotic stability." Annales Polonici Mathematici 68.1 (1998): 31-50. <http://eudml.org/doc/270275>.

@article{KatarzynaHorbacz1998,

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.},

author = {Katarzyna Horbacz},

journal = {Annales Polonici Mathematici},

keywords = {dynamical systems; Markov operator; asymptotic stability; evolution of measures; randomly chosen dynamical systems; invariant measure; transition operator},

language = {eng},

number = {1},

pages = {31-50},

title = {Randomly connected dynamical systems - asymptotic stability},

url = {http://eudml.org/doc/270275},

volume = {68},

year = {1998},

}

TY - JOUR

AU - Katarzyna Horbacz

TI - Randomly connected dynamical systems - asymptotic stability

JO - Annales Polonici Mathematici

PY - 1998

VL - 68

IS - 1

SP - 31

EP - 50

AB - 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.

LA - eng

KW - dynamical systems; Markov operator; asymptotic stability; evolution of measures; randomly chosen dynamical systems; invariant measure; transition operator

UR - http://eudml.org/doc/270275

ER -

## References

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- [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. Zbl0784.58005
- [8] A. Lasota and J. A. Yorke, Lower bound technique for Markov operators and iterated function systems, Random Comput. Dynamics 2 (1994), 41-77. Zbl0804.47033
- [9] T. Szarek, Iterated function systems depending on previous transformation, Univ. Iagell. Acta Math., to appear. Zbl0888.47016

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