We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D（μω） be its dimension of the sample measure, then we pr...We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D（μω） be its dimension of the sample measure, then we prove a formula relating D（μω） to the entropy and Lyapunov exponents of the random system, where D （μω） is dimHμω, dimBμm, or dimBμm.展开更多
The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are p...The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are proved. Its application in numerical simulation of differential equation is also considered. The upper semi-continuity of attractors in set value maps under the perturbation is used to show the reasonable of subdivision algorithm and interval arithmetic in numerical simulation of differential equation.展开更多
基金Partially supported by NSFC(10571130)NSFC(10501033) and SRFDP of China.
文摘We consider random systems generated by two-sided compositions of random surface diffeomorphisms, together with an ergodic Borel probability measure μ. Let D（μω） be its dimension of the sample measure, then we prove a formula relating D（μω） to the entropy and Lyapunov exponents of the random system, where D （μω） is dimHμω, dimBμm, or dimBμm.
基金Project supported by the National Natural Science Foundation of China (No.10571130)
文摘The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are proved. Its application in numerical simulation of differential equation is also considered. The upper semi-continuity of attractors in set value maps under the perturbation is used to show the reasonable of subdivision algorithm and interval arithmetic in numerical simulation of differential equation.
