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Exponential attractors for random dynamical systems and applications [PDF]
, 2013 The paper is devoted to constructing a random exponential attractor for some classes of stochastic PDE's. We first prove the existence of an exponential attractor for abstract random dynamical systems and study its dependence on a parameter and then ...
Armen Shirikyan, Sergey Zelik
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On the Concept of Complexity of Random Dynamical Systems [PDF]
International Journal of Modern Physics B, 1998 We show how to introduce a characterization the "complexity" of random dynamical systems. More precisely we propose a suitable indicator of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by these systems.
Vittorio Loreto +2 more
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Random conformal dynamical systems [PDF]
Geometric and Functional Analysis, 2005 We consider random dynamical systems such as groups of conformal transformations with a probability measure, or transversaly conformal foliations with a Laplace operator along the leaves, in which case we consider the holonomy pseudo-group. We prove that either there exists a measure invariant under all the elements of the group (or the pseudo-group ...
Bertrand Deroin, Victor Kleptsyn
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Anomalous Diffusion in Random Dynamical Systems [PDF]
Physical Review Letters, 2019 10 pages, 7 ...
Rainer Klages +3 more
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Random dynamical systems, entropies and information [PDF]
Physica A: Statistical Mechanics and its Applications, 2001 Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general consensus on what should be the correct indicator for complexity is still not reached.
Maurizio Serva
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Local Entropy Theory of a Random Dynamical System [PDF]
, 2011 In this paper we extend the notion of a continuous bundle random dynamical system to the setting where the action of $\R$ or $\N$ is replaced by the action of an infinite countable discrete amenable group.
A. H. Dooley, Guohua Zhang
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Stability index of linear random dynamical systems [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2021 Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution.
Anna Cima +2 more
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Gradient Infinite-Dimensional Random Dynamical Systems [PDF]
SIAM Journal on Applied Dynamical Systems, 2012 In this paper we introduce the concept of a gradient random dynamical system as a random semiflow possessing a continuous random Lyapunov function which describes the asymptotic regime of the system.
Tomás Caraballo +2 more
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Random chain recurrent sets for random dynamical systems [PDF]
Dynamical Systems, 2009 It is known by the Conley's theorem that the chain recurrent set $CR( )$ of a deterministic flow $ $ on a compact metric space is the complement of the union of sets $B(A)-A$, where $A$ varies over the collection of attractors and $B(A)$ is the basin of attraction of $A$. It has recently been shown that a similar decomposition result holds for random
Xiaopeng Chen, Jinqiao Duan
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Generating a Random Dynamical System
Asian Journal of Applied Science and Engineering, 2014 In this paper we shall create a new random dynamical system from old one. One of the most important of them, is the product of two random dynamical systems, which is also random dynamical system. This technique will be very important to detailed study of the random dynamical system.
Salah H. Abid, Ihsan Jabbar Kadhim
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