Related papers: Existence of random invariant periodic curves via …
We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical…
We study dynamical systems forced by a combination of random and deterministic noise and provide criteria, in terms of Lyapunov exponents, for the existence of random attractors with continuous structure in the fibres. For this purpose, we…
This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of…
We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…
In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a $C^1$ perfect cocycle on a cylinder using a random invariant set, the Lyapunov…
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…
Motivated by studying stochastic systems with non-Gaussian L\'evy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump discontinuities in time. A multiplicative ergodic theorem…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
We consider impulsive semiflows and establish sufficient conditions to the existence of invariant measures. Namely, the impulsive set and its image are both submanifolds of codimension one that are transversal to the flow direction.…
This article reviews a generous sampling of both classical and more recent results on the interplay between measurable and topological dynamics. In the first part we have surveyed the strong analogies between ergodic theory and topological…
We propose as a generalization of an idea of Ruelle to describe turbulent fluid flow a chaotic hypothesis for reversible dissipative many particle systems in nonequilibrium stationary states in general. This implies an extension of the…
This paper is concerned with the existence and uniqueness of random periodic solutions for stochastic differential equations (SDEs), where the drift terms involved need not to be uniformly dissipative. On the one hand, via the reflection…
A pseudorandom point in an ergodic dynamical system over a computable metric space is a point which is computable but its dynamics has the same statistical behavior as a typical point of the system. It was proved in [Avigad et al. 2010,…
Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently…
In this paper, we study Random Dynamical Systems (RDSs) of homeomorphisms on the circle without a finite orbit. We characterize the topological dynamics of the associated semigroup by identifying the existence of invariant sets which are…
A homogenization problem of infinite dimensional diffusion processes indexed by ${\mathbf Z}^d$ having periodic drift coefficients is considered. By an application of the uniform ergodic theorem for infinite dimensional diffusion processes…
In this paper, we are concerned with the existence of invariant curves of the planar twist mappings where the perturbations are almost periodic. As an application, the existence of almost periodic solutions and the boundedness of all…
In this paper, we define random quasi-periodic paths for random dynamical systems and quasi-periodic measures for Markovian semigroups. We give a sufficient condition for the existence and uniqueness of random quasi-periodic paths and…
Using continuation methods, we study the global solution structure of periodic solutions for a class of periodically forced equations, generalizing the case of relativistic pendulum. We obtain results on the existence and multiplicity of…
We provide conditions which guarantee that ergodic measures are dense in the simplex of invariant probability measures of a dynamical system given by a continuous map acting on a Polish space. Using them we study generic properties of…