Invariant Measures for Uncountable Random Interval Homeomorphisms
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Janusz Morawiec [1] ; Tomasz Szarek [2]
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[1] University of Silesia
University of Silesia
Katowice, Polonia
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[2] University of Technology
University of Technology
Rusia
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 4, 2023
- Idioma: inglés
- Enlaces
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Resumen
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, neither 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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