Kgs And Zakharov Of Lattice Systems, Global Attractors And Nuclear Cross Section

Dynamical systems(finite and infinite-dimensional) play an important part in nonlinear science, which investigate the dynamical behavior of natural phenomena with the time varying. During the past decades,considerable researches have been done,and many achievements have been obtained as well.As to the autonomous infinite-dimensional dynamical systems,we often use global attractors to describe its long time behavior.While for the non-autonomous infinite-dimensional dynamical systems,we usually apply uniform attractors or kernel sections(can be both regarded as generalizations of the notation of global attractors) to describe its long time behavior. However,whether global attractors or uniform attractors and kernel sections,we primarily study them by means of their existence,Kolmogorov-entropy,upper semicontinuity,Hausdorff dimension and fractal dimension,etc.As a type of typical infinite-dimensional ordinary differential systems,lattice dynamical systems (autonomous and non-autonomous) appeal to many mathematicians and physicians due to its wide applications in many fields such as chemical reaction theory,material science,laser systems, electrical engineering and so on.In recent years,there were many researchers had studied the unique existence as well as other properties of the solutions of lattice dynamical systems.For example, not only the existence,Kolmogorov-entropy,upper semicontinuity and fractal dimension of global attractors for autonomous lattice dynamical systems had been leant;but also the existence, Kolmogorov-entropy,upper semicontinuity and fractal dimension for uniform attractors or kernel sections for non-autonomous lattice dynamical systems had been investigated.In addition, retard and stochastic lattice dynamical systems have been recently considered too.This paper is organized as follows:In the first chapter,we make a simple introduction to "Dynamical Systems","Infinite-Dimensional Dynamical Systems" and "Lattice Dynamical Systems".Some notations and preliminaries relate to the paper are described in the second chapter.Fractal dimension of global attractors for autonomous Klein-Gordon-Schr(o|¨)dinger lattice dynamical systems is estimated and an upper bound is obtained in the third chapter.Finally,in the fourth chapter,the existence of kernel sections for non-autonomous Zakharov lattice dynamical systems is proved at first,and then an upper bound of fractal dimension of the kernel sections is obtained as well as the upper semicontinuity of the kernel sections is established.