The existence of pullback attractors for semi-uniformly dissipative dynamical systems under some asymptotic compactness assumptions is considered.A sufficient condition for the existence of pullback attractors is pres...The existence of pullback attractors for semi-uniformly dissipative dynamical systems under some asymptotic compactness assumptions is considered.A sufficient condition for the existence of pullback attractors is presented.Then,the results are applied to non-autonomous 2D Navier-Stokes equations.展开更多
The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are establi...The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are established. By making use of these results, it is feasible to get uniform estimation of the Lyapunov exponent of some special systems even under non-uniform hypotheses展开更多
In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity ...In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation and observation function are ignorable in some measure-theoretical sense. The theorems extend the classical results which have been established for continuous transformations and continuous observation functions.展开更多
基金National Natural Science Foundations of China(No.70773075,No.10871040)Chinese Universities Scientific Fund(No.10D10911)+1 种基金State key Program of National Science of China(No.11031003)Mathematical Tianyuan Foundation of China(No.11026136)
文摘The existence of pullback attractors for semi-uniformly dissipative dynamical systems under some asymptotic compactness assumptions is considered.A sufficient condition for the existence of pullback attractors is presented.Then,the results are applied to non-autonomous 2D Navier-Stokes equations.
文摘The aim of this paper is to extend the semi-uniform ergodic theorem and semi-uniform sub-additive ergodic theorem to skew-product quasi-flows. Furthermore, more strict inequalities about these two theorems are established. By making use of these results, it is feasible to get uniform estimation of the Lyapunov exponent of some special systems even under non-uniform hypotheses
基金Supported by National Natural Science Foundation of China(NSFC)(Grant Nos.11671382 and 11301512)Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)+1 种基金CAS Key Project of Frontier Sciences(Grant No.QYZDJ-SSW-JSC003)National Center for Mathematics and Interdisciplinary Sciences。
文摘In this paper, for a discontinuous skew-product transformation with the integrable observation function, we obtain uniform ergodic theorem and semi-uniform ergodic theorem. The main assumptions are that discontinuity sets of transformation and observation function are ignorable in some measure-theoretical sense. The theorems extend the classical results which have been established for continuous transformations and continuous observation functions.