Centre manifolds for infinite dimensional random dynamical systems

2018 ◽  
Vol 34 (2) ◽  
pp. 334-355 ◽  
Author(s):  
Xiaopeng Chen ◽  
Anthony J. Roberts ◽  
Jinqiao Duan
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Infinite Dimensional ◽  
Centre Manifolds

Random dynamical systems with jumps

2004 ◽  
Vol 41 (03) ◽  
pp. 890-910 ◽  
Author(s):  
Katarzyna Horbacz
Keyword(s):  
Dynamical Systems ◽  
Iterated Function System ◽  
Infinite Family ◽  
Learning Systems ◽  
Random Dynamical Systems ◽  
Infinite Dimensional ◽  
Markov Operators ◽  
Iterated Function ◽  
Random Evolutions ◽  
Deterministic Dynamical Systems

We consider random dynamical systems with randomly chosen jumps on infinite-dimensional spaces. The choice of deterministic dynamical systems and jumps depends on a position. The system generalizes dynamical systems corresponding to learning systems, Poisson driven stochastic differential equations, iterated function system with infinite family of transformations and random evolutions. We will show that distributions which describe the dynamics of this system converge to an invariant distribution. We use recent results concerning asymptotic stability of Markov operators on infinite-dimensional spaces obtained by T. Szarek.

scholarly journals Infinite Dimensional Random Dynamical Systems and Their Applications

2008 ◽  
pp. 2815-2874
Author(s):  
Franco Flandoli ◽  
Peter Kloeden ◽  
Andrew Stuart
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Infinite Dimensional

scholarly journals Gradient Infinite-Dimensional Random Dynamical Systems

2012 ◽  
Vol 11 (4) ◽  
pp. 1817-1847 ◽  
Author(s):  
Tomás Caraballo ◽  
José A. Langa ◽  
Zhenxin Liu
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Infinite Dimensional

Random dynamical systems with jumps

2004 ◽  
Vol 41 (3) ◽  
pp. 890-910 ◽  
Author(s):  
Katarzyna Horbacz
Keyword(s):  
Dynamical Systems ◽  
Iterated Function System ◽  
Infinite Family ◽  
Learning Systems ◽  
Random Dynamical Systems ◽  
Infinite Dimensional ◽  
Markov Operators ◽  
Iterated Function ◽  
Random Evolutions ◽  
Deterministic Dynamical Systems

We consider random dynamical systems with randomly chosen jumps on infinite-dimensional spaces. The choice of deterministic dynamical systems and jumps depends on a position. The system generalizes dynamical systems corresponding to learning systems, Poisson driven stochastic differential equations, iterated function system with infinite family of transformations and random evolutions. We will show that distributions which describe the dynamics of this system converge to an invariant distribution. We use recent results concerning asymptotic stability of Markov operators on infinite-dimensional spaces obtained by T. Szarek.

scholarly journals On the Oseledets-splitting for infinite-dimensional random dynamical systems

2018 ◽  
Vol 23 (3) ◽  
pp. 1219-1242
Author(s):  
Kening Lu ◽  
◽  
Alexandra Neamţu ◽  
Björn Schmalfuss ◽  
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Infinite Dimensional
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