Invariant Measures for Uncountable Random Interval Homeomorphisms

Tomasz Szarek; Janusz Morawiec

doi:10.1007/s12346-023-00822-y

Invariant Measures for Uncountable Random Interval Homeomorphisms

Abstract

A necessary and sufficient condition for the iterated function system { f (·, ω) | ω ∈ } with probability P to have exactly one invariant measure μ∗ with μ∗((0, 1)) = 1 is given. The main novelty lies in the fact that we only require the transformations f (·, ω) to be increasing homeomorphims, without any smoothness condition, nei- ther we impose conditions on the cardinality of . In particular, positive Lyapunov exponents conditions are replaced with the existence of solutions to some functional inequalities. The stability and strong law of large numbers of the considered system are also proven.

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Authors (2)

Tomasz Szarek prof. dr hab. inż.
Janusz Morawiec dr hab.

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Keywords

ITERATED FUNCTION SYSTEMS · INVARIANT MEASURES · STABILITY · STRONG LAW OF LARGE NUMBERS · FUNCTIONAL EQUATIONS

Details

Category:

Articles

Type:

artykuły w czasopismach

Published in:

Qualitative Theory of Dynamical Systems no. 22,
ISSN: 1575-5460

Language:

English

Publication year:

2023

Bibliographic description:

Szarek T., Morawiec J.: Invariant Measures for Uncountable Random Interval Homeomorphisms// Qualitative Theory of Dynamical Systems -Vol. 22,iss. 4 (2023),

DOI: