On Random Attractors for Mixing Type Systems ∗

نویسنده

  • A. Shirikyan
چکیده

The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that the support of the unique invariant measure is the minimal random point attractor. The results obtained apply to the randomly forced 2D Navier–Stokes system.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

upper semicontinuity of attractors for small random perturbations of dynamical systems

The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an −small random term and certain hypotheses are satisfied, the upper semicontinuity of the random attractors is obtained as goes to zero. The results are applied to the Navier-Stokes equations and a problem of reaction-diffusion type, both pertur...

متن کامل

Minimal attractors and bifurcations of random dynamical systems

We consider attractors for certain types of random dynamical systems. These are skew-product systems whose base transformations preserve an ergodic invariant measure. We discuss definitions of invariant sets, attractors and invariant measures for deterministic and random dynamical systems. Under assumptions that include, for example, iterated function systems, but that exclude stochastic differ...

متن کامل

Upper Semicontinuity of Random Attractors for Non-compact Random Dynamical Systems

The upper semicontinuity of random attractors for non-compact random dynamical systems is proved when the union of all perturbed random attractors is precompact with probability one. This result is applied to the stochastic Reaction-Diffusion with white noise defined on the entire space Rn.

متن کامل

Weak Random Attractors

We deene point attractors and set attractors for random dynamical systems via convergence in probability forward in time. This deenition of a set attractor is weaker than the usual one via almost sure pullback convergence. We derive basic properties of our weak random attractors such as uniqueness, support of invariant measures and invari-ance under (random) coordinate transformations. The noti...

متن کامل

Simplest 3D continuous-Time quadratic Systems as Candidates for Generating multiscroll Chaotic attractors

In many situations, the existence of several equilibrium points in a dynamical system makes its dynamics more complex and allows some special structures. Examples include the well-known multiscroll attractors ([Wang, 2009; Qi et al., 2008; Liu & Chen, 2004; Li, 2008; Wang et al., 2009; Lü et al., 2008; Yu et al., 2006; Yu et al., 2008, 2010a; Wang & Chen, 2012] and references therein) such as c...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004