集值映射及其应用

基金项目: 国家自然科学基金资助项目(10571130)

Set Value Mapping and Its Application

Department of Mathematics, Suzhou University, Suzhou, Jiangsu 215006, P. R. China

摘要: 考虑集值映射的动力学，证明了对于上半连续的集值映射在一定条件下吸引子的存在性及吸引子在扰动下的上半连续性，进一步考虑集值映射在微分方程数值模拟中的应用．利用集值映射的吸引子在扰动下的上半连续性，阐明微分方程数值模拟中的次分算法及区间算法的合理性．
- 集值映射 /
- 吸引子 /
- 上半连续性
Abstract: 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 were proved. Its application in numerical simulation of differential equation was also considered. The upper semi-continuity of attractors in set value maps under the perturbation was used to show the reasonable of subdivision algorithm and interval arithmetic in numerical simulation of differential equation.
- set value mapping /
- attractor /
- upper semi-continuity

[1]	Kloeden P E,Lorenz J.Stable attracting sets in dynamical systems and in their one-step discretizations[J].SIAM J Numer Anal,1986,23(5):986—995. doi: 10.1137/0723066
[2]	Dellnitz M,Hohmann A.A subdivision algorithm for the computation of unstable manifold and global attractors[J].Numer Math,1997,75(3):293—317. doi: 10.1007/s002110050240
[3]	Caraballo T,Langa J A.On the upper semicontinuity of cocyle attractors for non-autonomous and random dynamical systems[J].Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis,2003,10(4):491—513.
[4]	Caraballo T,Langa J A,Robinson J C.On the upper semicontinuity of attractors for small random perturbations of dynamical systems[J].Communication in PDEs,1998,23(9/10):1557—1581. doi: 10.1080/03605309808821394