相关论文: Stochastic stability of diffeomorphisms with domin…

For a class of dynamical systems, called the axiom-A systems, Sinai, Ruelle and Bowen showed the existence of an invariant measure (SRB measure) weakly attracting the temporal average of any initial distribution that is absolutely…

We study the simplicity of the Lyapunov spectrum of partially hyperbolic diffeomorphisms. We prove that a class of volume-preserving partially hyperbolic diffeomorphisms is $C^r$-accumulated by $C^2$-open sets with simple spectrum. Also we…

In this paper we mainly deal with an invariant (ergodic) hyperbolic measure $\mu$ for a diffeomorphism $f,$ assuming that $f$ is just $C^1$ and for $\mu$ a.e. $x$, the sum of Oseledec spaces corresponding to negative Lyapunov exponents…

Random dynamical systems with countably many maps which admit countable Markov partitions on complete metric spaces such that the resulting Markov systems are uniformly continuous and contractive are considered. A non-degeneracy and a…

In this article we study (possibly degenerate) stochastic differential equations (SDE) with irregular (or discontiuous) coefficients, and prove that under certain conditions on the coefficients, there exists a unique almost everywhere…

We introduce the notion of nonuniform center bunching for partially hyperbolic diffeomorphims, and extend previous results by Burns--Wilkinson and Avila--Santamaria--Viana. Combining this new technique with other constructions, we prove…

We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…

This paper extends deterministic notions of Strong Stability Preservation (SSP) to the stochastic setting, enabling nonlinearly stable numerical solutions to stochastic differential equations (SDEs) and stochastic partial differential…

For Anosov diffeomorphisms on the $3$-torus which are strongly partially hyperbolic with expanding center, we construct systems of strong unstable and center stable Margulis measures which are holonomy-invariant. This allows us to obtain a…

We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a…

We develop a general framework for establishing non-uniqueness of stationary measures for stochastically forced dynamical systems possessing an almost surely invariant submanifold. Our main abstract result provides sufficient conditions for…

This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mechanics. We adopt a new point of view which has emerged progressively in recent years, and which takes…

We construct a smooth nontrivial mixed partially hyperbolic system and explicitly identify its skeleton. This example shares characteristics with the classical examples. Moreover, the support of each physical measure contains three fixed…

In this paper, the problem of stability in terms of two measures is considered for a class of stochastic partial differential delay equations with switching. Sufficient conditions for stability in terms of two measures are obtained based on…

This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for…

In this paper, we mainly study the long-time dynamical behaviors of 2D nonlocal stochastic Swift-Hohenberg equations with multiplicative noise from two perspectives. Firstly, by adopting the analytic semigroup theory, we prove the upper…

The stability problem in terms of two measures for semiflows in space conv(R^n) was investigated. On the basis of comparison principle the obtained result is used to study the stability criteria for a certain semiflow in space conv(R^n).…

In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these…

We prove that if $t \mapsto u(t) \in \mathrm {BV}(\R)$ is the entropy solution to a $N \times N$ strictly hyperbolic system of conservation laws with genuinely nonlinear characteristic fields \[ u_t + f(u)_x = 0, \] then up to a countable…