相关论文: Stochastic stability of diffeomorphisms with domin…
We study the asymptotic behaviour of stationary densities of one-dimensional random diffeomorphisms, at the boundaries of their support, which correspond to deterministic fixed points of extremal diffeomorphisms. In particular, we show how…
It is well-known that SRB and equilibrium measures for uniformly hyperbolic flows admit a product structure in terms of measures on stable and unstable leaves with scaling properties given by the potential function. We describe a…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
We prove that every dynamically coherent plaque expansive partially hyperbolic diffeomorphism is topologically stable with respect to the central foliation (in short, {\em plaque topologically stable}). Next, we study partially hyperbolic…
We consider a stochastic lattice Cahn-Hilliard equation with nonautonomous nonlinear noise. First, we prove the existence of pullback random attractors in $\ell^2$ for the generated nonautonomous random dynamical system. Then, we construct…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
We introduce a new measure of instability of area-preserving twist diffeomorphisms, which generalizes the notions of angle of splitting of separatrices, and flux through a gap of a Cantori. As an example of application, we establish a sharp…
We consider Glauber-type stochastic dynamics of continuous systems \cite{BCC02}, \cite{KL03}, a particular case of spatial birth-and-death processes. The dynamics is defined by a Markov generator in such a way that Gibbs measures of Ruelle…
In this paper, we define and study unstable measure theoretic pressure for C^1-smooth partially hyperbolic diffeomorphisms with sub-additive potentials. For any ergodic measure, we show that this unstable metric pressure equals the…
In this article we study some statistical aspects of surface diffeomorphisms. We first show that for a $C^1$ generic diffeomorphism, a Dirac invariant measure whose \emph{statistical basin of attraction} is dense in some open set and has…
It is well-known that the Manneville-Pomeau map with a parabolic fixed point of the form $x\mapsto x+x^{1+\alpha} \mod 1$ is stochastically stable for $\alpha\ge 1$ and the limiting measure is the Dirac measure at the fixed point. In this…
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…
When high-dimensional non-uniformly hyperbolic chaotic systems undergo dynamical perturbations, their long-time statistics are generally observed to respond differentiably with respect to the perturbation. Although important in…
We develop a general geometric method to establish the existence of positive Lyapunov exponents for a class of skew products. The technique is applied to show non-uniform hyperbolicity of some conservative partially hyperbolic…
A particular type of random dynamical processes is considered, in which the stochasticity is introduced through randomly fluctuating parameters. A method of local multipliers is developed for treating the local stability of such dynamical…
A better understanding of the instability margin will eventually optimize the operational range for safety-critical industries. In this paper, we investigate the almost-sure exponential asymptotic stability of the trivial solution of a…
Given a dynamical system, a characteristic measure is a Borel probability measure invariant under all of its automorphisms. Frisch and Tamuz asked if every symbolic system supports such a measure. Motivated by this problem, we study the…
In this paper we consider $C^{1}$ diffeomorphisms on compact Riemannian manifolds of any dimension that admit a dominated splitting $E^{cs} \oplus E^{cu}.$ We prove that if the Lyapunov exponents along $E^{cu}$ are positive for Lebesgue…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
This article is dedicated to the study of diagonal hyperbolic systems in one space dimension, with cumulative distribution functions, or more generally nonconstant monotonic bounded functions, as initial data. Under a uniform strict…