Typical Behaviour of Random Interval Homeomorphisms

J 2021

Typical Behaviour of Random Interval Homeomorphisms

BRADÍK, Jaroslav a Samuel Joshua ROTH

Základní údaje

Originální název

Typical Behaviour of Random Interval Homeomorphisms

Autoři

BRADÍK, Jaroslav (203 Česká republika, domácí) a Samuel Joshua ROTH (840 Spojené státy, garant, domácí)

Vydání

Qualitative Theory of Dynamical Systems, Basel, Switzerland, Springer International Publishing, 2021, 1575-5460

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Švýcarsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Qualitative Theory of Dynamical Systems

Impakt faktor

Impact factor: 0.931

Kód RIV

RIV/47813059:19610/21:A0000099

Organizační jednotka

Matematický ústav v Opavě

DOI

https://doi.org/10.1007/s12346-021-00509-2

UT WoS

000686649500001

EID Scopus

2-s2.0-85112421281

Klíčová slova anglicky

Random dynamical systems; Interval homeomorphisms; Singular stationary measures; Residual set

Štítky

MÚ, SGS-18-2019

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 29. 3. 2022 09:33, Mgr. Aleš Ryšavý

Anotace

V originále

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.

Citovat

BRADÍK, Jaroslav a Samuel Joshua ROTH. Typical Behaviour of Random Interval Homeomorphisms. Qualitative Theory of Dynamical Systems. Basel, Switzerland: Springer International Publishing, 2021, roč. 20, č. 3, s. "73-1"-"73-20", 20 s. ISSN 1575-5460. Dostupné z: https://doi.org/10.1007/s12346-021-00509-2.

@article{54501,
   author = {Bradík, Jaroslav and Roth, Samuel Joshua},
   article_location = {Basel, Switzerland},
   article_number = {3},
   doi = {https://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 a Samuel Joshua ROTH. Typical Behaviour of Random Interval Homeomorphisms. \textit{Qualitative Theory of Dynamical Systems}. Basel, Switzerland: Springer International Publishing, 2021, roč.~20, č.~3, s.~''73-1''-''73-20'', 20 s. ISSN~1575-5460. Dostupné z: https://doi.org/10.1007/s12346-021-00509-2.

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