2021
Typical Behaviour of Random Interval Homeomorphisms
BRADÍK, Jaroslav and Samuel Joshua ROTHBasic information
Original name
Typical Behaviour of Random Interval Homeomorphisms
Authors
BRADÍK, Jaroslav (203 Czech Republic, belonging to the institution) and Samuel Joshua ROTH (840 United States of America, guarantor, belonging to the institution)
Edition
Qualitative Theory of Dynamical Systems, Basel, Switzerland, Springer International Publishing, 2021, 1575-5460
Other information
Language
English
Type of outcome
Article in a journal
Field of Study
10101 Pure mathematics
Country of publisher
Switzerland
Confidentiality degree
is not subject to a state or trade secret
References:
Impact factor
Impact factor: 0.931
RIV identification code
RIV/47813059:19610/21:A0000099
Organization unit
Mathematical Institute in Opava
UT WoS
000686649500001
EID Scopus
2-s2.0-85112421281
Keywords in English
Random dynamical systems; Interval homeomorphisms; Singular stationary measures; Residual set
Tags
Tags
International impact, Reviewed
Changed: 29/3/2022 09:33, Mgr. Aleš Ryšavý
Abstract
In the original language
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.