Typical Behaviour of Random Interval Homeomorphisms
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Bradík, Jaroslav [1] ; Roth, Samuel [1]
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[1] Silesian University in Opava
Silesian University in Opava
Chequia
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- Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 20, Nº 3, 2021
- Idioma: inglés
- DOI: 10.1007/s12346-021-00509-2
- Enlaces
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Resumen
We consider the typical behaviour of random dynamical systems of order-preserving interval homeomorphisms with a positive Lyapunov exponent condition at the endpoints. Our study removes any requirement for continuous differentiability save the existence of finite derivatives of the homeomorphisms at the endpoints of the interval. We construct a suitable Baire space structure for this class of systems. Generically within this Baire space, we show that the stationary measure is singular with respect to the Lebesgue measure, but has full support on [0, 1]. This provides an answer to a question raised by Alsedà and Misiurewicz.
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Referencias bibliográficas
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