Related papers: Noise induced dissipation in Lebesgue-measure pres…
We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour…
We introduce a new characteristics of chaoticity of classical and quantum dynamical systems by defining the notion of the dissipation time which enables us to test how the system responds to the noise and in particular to measure the speed…
We introduce the notion of the relaxation time for noisy quantum maps on the 2d-dimensional torus - a generalization of previously studied dissipation time. We show that relaxation time is sensitive to the chaotic behavior of the…
In this paper, we investigate the linearly damped KdV equation on the one-dimensional torus $\mathbb{T}$, perturbed by a multiplicative L\'{e}vy noise. For any damping coefficient $\gamma > 0$, we establish the existence and uniqueness of a…
We obtain large deviation results for non-uniformly expanding maps with non-flat singularities or criticalities and for partially hyperbolic non-uniformly expanding attracting sets. That is, given a continuous function we consider its space…
We study nonlinear wave equations perturbed by transport noise acting either on the displacement or on the velocity. Such noise models random advection and, under suitable scaling of space covariance, may generate an effective dissipative…
The stochastic $p$-Laplace equation with multiplicative transport noise is studied on the torus $\mathbb T^d\, (d\geq 2)$. It is shown that the dissipation is enhanced by transport noise in both the averaged sense and the pathwise sense.
We investigate theoretically and numerically transport noise-induced diffusion in flows on the sphere. Previous analysis on the torus demonstrated that suitably chosen transport noise in the Euler equations leads to diffusive behavior…
A new discrete time-reversible map of a unit square onto itself is proposed. The map comprises of piecewise linear two-dimensional operations, and is able to represent the macroscopic features of both equilibrium and nonequilibrium…
In this paper, we show that suitable transport noises produce anomalous dissipation of both enstrophy of solutions to 2D Navier-Stokes equations and of energy of solutions to diffusion equations in all dimensions. The key ingredients are…
Using a nonperturbative weak noise approach we investigate the interference of noise and chaos in simple 1D maps. We replace the noise-driven 1D map by an area-preserving 2D map modelling the Poincare sections of a conserved dynamical…
The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied. We characterize the smallest closed invariant subspace for this model and show that the dynamics restricted to that subspace is ergodic. In…
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random…
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of…
We consider a parametrised perturbation of a $\mathscr C^r$ diffeomorphism on a closed smooth Riemannian manifold with $r\geq 1$, modeled by nonautonomous dynamical systems. A point without time averages for a (nonautonomous) dynamical…
The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the $L^2$-setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq…
In this article we present some results concerning natural dissipative perturbations of 3d Hamiltonian systems. Given a Hamiltonian system dx/dt = PdH, and a Casimir function S, we construct a symmetric covariant tensor g, so that the…
Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
In the first part of the note we analyze the long time behaviour of a two dimensional stochastic Navier--Stokes equations system on a torus with a degenerate, one dimensional noise. In particular, for some initial data and noises we…