scholarly journals Random Dynamical Systems with Jumps and with a Function Type Intensity

2016 ◽  
Vol 30 (1) ◽  
pp. 63-87
Author(s):  
Joanna Kubieniec
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Invariant Measure ◽  
Lipschitz Function ◽  
Random Dynamical Systems ◽  
Function Type ◽  
Polish Spaces

AbstractIn paper [4] there are considered random dynamical systems with randomly chosen jumps acting on Polish spaces. The intensity of this process is a constant λ. In this paper we formulate criteria for the existence of an invariant measure and asymptotic stability for these systems in the case when λ is not constant but a Lipschitz function.

scholarly journals Strong Unique Ergodicity of Random Dynamical Systems on Polish Spaces

2016 ◽  
Vol 30 (1) ◽  
pp. 129-142
Author(s):  
Paweł Płonka
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Unique Ergodicity ◽  
Random Dynamical Systems ◽  
Random Measures ◽  
Polish Spaces

AbstractIn this paper we want to show the existence of a form of asymptotic stability of random dynamical systems in the sense of L. Arnold using arguments analogous to those presented by T. Szarek in [6], that is showing it using conditions generalizing the notion of tightness of measures. In order to do that we use tightness theory for random measures as developed by H. Crauel in [2].

scholarly journals Mixing and observation for Markov operator cocycles*

Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 66-83
Author(s):  
Fumihiko Nakamura ◽  
Yushi Nakano ◽  
Hisayoshi Toyokawa
Keyword(s):  
Dynamical Systems ◽  
Asymptotic Stability ◽  
Markov Operator ◽  
Random Dynamical Systems ◽  
Asymptotically Periodic ◽  
Definition Of

Abstract We consider generalized definitions of mixing and exactness for random dynamical systems in terms of Markov operator cocycles. We first give six fundamental definitions of mixing for Markov operator cocycles in view of observations of the randomness in environments, and reduce them into two different groups. Secondly, we give the definition of exactness for Markov operator cocycles and show that Lin’s criterion for exactness can be naturally extended to the case of Markov operator cocycles. Finally, in the class of asymptotically periodic Markov operator cocycles, we show the Lasota–Mackey type equivalence between mixing, exactness and asymptotic stability.

VARIATIONAL PRINCIPLE FOR SUBADDITIVE SEQUENCE OF POTENTIALS IN BUNDLE RANDOM DYNAMICAL SYSTEMS

2009 ◽  
Vol 09 (02) ◽  
pp. 205-215 ◽  
Author(s):  
XIANFENG MA ◽  
ERCAI CHEN
Keyword(s):  
Dynamical Systems ◽  
Variational Principle ◽  
Multifractal Analysis ◽  
Weak Condition ◽  
Random Dynamical Systems ◽  
Topological Pressure ◽  
Set Up

The topological pressure is defined for subadditive sequence of potentials in bundle random dynamical systems. A variational principle for the topological pressure is set up in a very weak condition. The result may have some applications in the study of multifractal analysis for random version of nonconformal dynamical systems.

Noise-induced unstable dimension variability and transition to chaos in random dynamical systems

2003 ◽  
Vol 67 (2) ◽  
Author(s):  
Ying-Cheng Lai ◽  
Zonghua Liu ◽  
Lora Billings ◽  
Ira B. Schwartz
Keyword(s):  
Dynamical Systems ◽  
Random Dynamical Systems ◽  
Transition To Chaos
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