Typical Behaviour of Random Interval Homeomorphisms

@article{54501,
   author = {Bradík, Jaroslav and Roth, Samuel Joshua},
   article_location = {Basel, Switzerland},
   article_number = {3},
   doi = {http://dx.doi.org/10.1007/s12346-021-00509-2},
   keywords = {Random dynamical systems; Interval homeomorphisms; Singular stationary measures; Residual set},
   language = {eng},
   issn = {1575-5460},
   journal = {Qualitative Theory of Dynamical Systems},
   title = {Typical Behaviour of Random Interval Homeomorphisms},
   url = {https://link.springer.com/article/10.1007%2Fs12346-021-00509-2},
   volume = {20},
   year = {2021}
}

TY  - JOUR
ID  - 54501
AU  - Bradík, Jaroslav - Roth, Samuel Joshua
PY  - 2021
TI  - Typical Behaviour of Random Interval Homeomorphisms
JF  - Qualitative Theory of Dynamical Systems
VL  - 20
IS  - 3
SP  - "73-1"-"73-20"
EP  - "73-1"-"73-20"
PB  - Springer International Publishing
SN  - 15755460
KW  - Random dynamical systems
KW  - Interval homeomorphisms
KW  - Singular stationary measures
KW  - Residual set
UR  - https://link.springer.com/article/10.1007%2Fs12346-021-00509-2
N2  - 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 Alseda and Misiurewicz.
ER  - 

BRADÍK, Jaroslav and Samuel Joshua ROTH. Typical Behaviour of Random Interval Homeomorphisms. \textit{Qualitative Theory of Dynamical Systems}. Basel, Switzerland: Springer International Publishing, 2021, vol.~20, No~3, p.~''73-1''-''73-20'', 20 pp. ISSN~1575-5460. Available from: https://dx.doi.org/10.1007/s12346-021-00509-2.