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张法勇 《高等学校计算数学学报》1999,21(1):32-37
1引言近年来.随着对无限维动力系统研究的深入,人们对非线性发展方程解的渐近性态了解得越来越多.例如对某些耗散的非线性发展方程,象Navier-Stokes方程、Kuramoto-Sivashin-sky方程等都存在整体的吸引子.系统的渐近性质和系统的复杂性完全由整体吸引子所确定(详细请参见[3]).与此同时,这类系统的有限维逼近也是人们非常关心的问题,在这方面已有许多工作,如J.K.Hale等人在[5]中基于有限元方法研究了某些非线性发展方程.得到了近似吸引子是上半连续的;C.M.Ellotta… 相似文献
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本文证明了在[1]中给出的参数区域内,对应的Lozi映射的奇怪吸引子Λ是横截及弱横截同宿点的闭包,并且Λ上任意两个双曲周期点形成横截及弱横截环;奇怪吸引子的吸引域的闭包就是双曲不动点X的稳定流形的闭包;进一步,吸引域恰好是ωs(X)及那些边界包含在ωs(X)及ωu(X)中区域的并,从而我们证明了对于Lozi映射,M.Benedicks和L.Carleson等的有关奇怪吸引子的吸引域的结构的猜测. 相似文献
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Let M be a manifold (possibly with boundary), and f:M→M be continuous. Call a closed invariant set A包含M an adic attractor of f if it attracts almost all points (in the sense of Lebesgue measure) and the restriction f|A is topologically conjugate to an adic system. Such an attractor A is called n-adic if the restriction flA can be topologically conjugate the n-adic system. 相似文献
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对于一个具有n-进位吸引子的区间连续映射,证明了:“n不是2的方幂”是该映射具有正拓扑熵的充分条件但不是必要条件;探讨了函数方程f~3(λx)=λf(x)的一类解,并证明这类解中的每一个成员都有3-进位吸引子. 相似文献
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Lozi映射奇怪吸引子的探讨 总被引:1,自引:0,他引:1
本文利用横截环理论,详细分析了Lozi映射的奇怪吸引子的存在性和结果,所得结果与数值结果相吻合,并解释了若干数值现象,从而进一步论证[1]所提出奇怪吸引子结论是合理的。 相似文献
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本文研究了非线性应变波方程与Schr(?)dinger方程耦合系统Cauchy问题吸引 子的正则性.获得了该系统在空间Eo中存在整体吸引子Ao,并且Ao与E1中的强吸 引子A1相等. 相似文献
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Alain Miranville 《Applications of Mathematics》2003,48(1):31-47
In this article we introduce the notion of a minimal attractor for families of operators that do not necessarily form semigroups. We then obtain some results on the existence of the minimal attractor. We also consider the nonautonomous case. As an application, we obtain the existence of the minimal attractor for models of Cahn-Hilliard equations in deformable elastic continua. 相似文献
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In this note, we study some properties of local random pull-back attractors on compact metric spaces. We obtain some relations between attractors and their fundamental neighborhoods and basins of attraction. We also obtain some properties of omega-limit sets, as well as connectedness of random attractors. A simple deterministic example is given to illustrate some confusing problems. 相似文献
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反应扩散方程组的最大吸引子通常是在不变区域内研究,如果不具有不变区域,或者去掉不变区域的限制而在全空间考虑这类问题,其结果如何?本文将证明一类反应扩散方程组在全空间最大吸引子的存在性,并对该吸引子的正则性进行了详细讨论,还给出了该吸引子的维数估计. 相似文献
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Abstract
In this paper, we establish the global fast dynamics for the derivative Ginzburg-Landau equation in two spatial dimensions.
We show the squeezing property and the existence of finite dimensional exponential attractors for this equation
* The author is supported by the Postdoctoral Foundation of China 相似文献
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O.IntroductionDynamicalbehavioroftheJosephsonjunctionhaslongbeenofinterestbecauseitreflectsarichvarietyofillterestingphenomena.Muchprogressonthedynamicsofasingle--pointjunctionandasystemofN-pointcoupledjunctions,whichcanberegardedasdiscretizedversionsofacontinuousJosephsonjunction,hasbeenmadebyexperiments,numericalcalculationsandtheoreticalanalysis["'15].ItiswellknownthattheequationofonecontinuousJosephsonjunctionisthedampedanddrivensine-Gordonequation,ofwhichtheexistenceanddimensionoftheglo… 相似文献
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Equi-attraction properties of the global attractors
of a family of set-valued dynamical systems {Gλ, λ∈Λ} with respect to a parameter λ∈Λ, where Λ is a compact metric space, are investigated. In particular, under appropriate
conditions, it is shown that the equi-attraction of the family
is equivalent to the continuity of
in λ with respect to the Hausdorff distance. An example involving differential inclusions is given.
Mathematics Subject Classifications (2000) Primary 47H17, 58F03, 34C20.
Desheng Li: Supported by NNSF of China (10251002) and NNSF of Gansu province (3ZS041-A25-006). 相似文献
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Attractors for a Nonclassical Diffusion Equation 总被引:11,自引:0,他引:11
Yue-long XiaoDepartment of Mathematics Xiangtan University Xiangtan China 《应用数学学报(英文版)》2002,18(2):273-276
Abstract For a nonclassical diffusion equation,the asymptotic behavior is investigated,and the existence ofa global attractor is proved. 相似文献
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We show that if f: M 3 → M 3 is an A diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal{B}$ with support $M_\mathcal{B}^2$ , then $\mathcal{B} = M_\mathcal{B}^2$ and there exists a k ≥ 1 such that (1) $M_\mathcal{B}^2$ is the disjoint union M 1 2 ? ? ? M k 2 of tame surfaces such that each surface M i 2 is homeomorphic to the 2-torus T 2; (2) the restriction of f k to M i 2 , i ∈ {1,..., k}, is conjugate to an Anosov diffeomorphism of the torus T 2. 相似文献