Related papers: Almost periodicity and periodicity for nonautonomo…

In this paper, we studied quasi-periodic and almost periodic homogenizations of integro-differential equations with Levy operators, which contain alpha stable Levy densities. This is the intermediate stage between the periodic…

Aperiodic order refers to the mathematical formalisation of quasicrystals. Substitutions and cut and project sets are among their main actors; they also play a key role in the study of dynamical systems, whether they are symbolic, generated…

In this paper, we propose a stochastic forward-backward-forward splitting algorithm and prove its almost sure weak convergence in real separable Hilbert spaces. Applications to composite monotone inclusion and minimization problems are…

This work is concerned with a singularly perturbed stochastic nonlinear wave equation with a random dynamical boundary condition. A splitting skill is used to derive the approximating equation of the system in the sense of probability…

In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…

In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin…

We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We…

Stochastic systems often exhibit multiple viable metastable states that are long-lived. Over very long timescales, fluctuations may push the system to transition between them, drastically changing its macroscopic configuration. In realistic…

We study localisation transition in a class of quasi-periodic systems that has two competing periodic scales. We show that such class of systems show a re-entrant localisation transition where the energy scale of transition is set by the…

The main aim of this paper is to consider the classes of quasi-asymptotically almost periodic functions and Stepanov quasi-asymptotically almost periodic functions in Banach spaces. These classes extend the well known classes of…

Many complex systems can spontaneously oscillate under non-periodic forcing. Such self-oscillators are commonplace in biological and technological assemblies where temporal periodicity is needed, such as the beating of a human heart or the…

In the setting of stochastic dynamical systems that eventually go extinct, the quasi-stationary distributions are useful to understand the long-term behavior of a system before evanescence. For a broad class of applicable continuous-time…

We develop a new theory of maximizing sets in dynamical systems, for the study of ergodic optimization in systems with weak hyperbolicity but where the Ma\~n\'e cohomology lemma does not hold. This leads to new solutions of the Typical…

We introduce a Hamiltonian dynamics for the description of long-range interacting systems in contact with a thermal bath (i.e., in the canonical ensemble). The dynamics confirms statistical mechanics equilibrium predictions for the…

In this paper, we first propose a concept of weighted pseudo-almost periodic functions on time scales and study some basic properties of weighted pseudo-almost periodic functions on time scales. Then, we establish some results about the…

We present a method to compute the stochastic reachability safety probabilities for high-dimensional stochastic dynamical systems. Our approach takes advantage of a nonparametric learning technique known as conditional distribution…

We investigate the dynamics of periodic non-autonomous discrete dynamical systems on uniform spaces and topological spaces, focusing on the extension of the classical Auslander-Yorke dichotomy to these settings. We prove various dichotomy…

We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged…

Quasi-stationary distributions, as discussed by Darroch & Seneta (1965), have been used in biology to describe the steady state behaviour of population models which, while eventually certain to become extinct, nevertheless maintain an…

This paper constructs a solvability theory for a system of stochastic partial differential equations. On account of the Kolmogorov continuity theorem, solutions are looked for in certain H\"older-type classes in which a random field is…