Random Attractor And Its Kolmogorov Entropy For Two Lattice Systems With Multiplicative White Noise

In recent years, with the rapid development of random dynamical system, randomdynamic system has become a hot subject to study the dynamic system in the field ofInternational. The random attractor is an important tool of the dynamic behavior of thestochastic diferential equation. This dissertation is devoted to the random attractor andits kolmogorov entropy for two lattice systems with multiplicative white noise.In chapter1, we introduce the history and the development of random dynamicalsystems, random attractor and kolmogorov entropy, and some preliminary results anddefinitions and frequently used inequalities, and the main research work for this paper.In chapter2, we consider a second-order lattice system with multiplicative whitenoise, and prove the existence of the random attractor for this system on Zk, and get anupper bounded of the Kolmogorov entropy of the random attractor.In chapter3, we consider the stochastic discrete long wave-short wave resonancelattice system with multiplicative white noise, and prove the existence of the randomattractor for this system on Zk,and get an upper bounded of the Kolmogorov entropyof the random attractor.