共查询到20条相似文献,搜索用时 109 毫秒
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本文讨论了双曲系统的稳定流形结构的稳定性,证明了 C~2自映射双曲不变集的局部稳定与非稳定流形结构相对 C~1扰动是稳定的. 相似文献
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引入部分双曲集的概念,证明了紧黎曼流形上的微分同胚在其部分双曲集的小邻域内具有如下形式的拟跟踪性:设f为紧黎曼流形M上的一个微分同胚,Λ为f的部分双曲集.则存在Λ的邻域O(Λ),使得对于任意ε>0,存在δ>0,使得f在O(Λ)中的任意δ-伪轨{x_k}k∈Z,存在点列{y_k}k∈Z,和中心向量列{u_k∈E_(xk)~c}k∈Z满足d(x_k,y_k)<ε,其中y_k=exp_(x_k)(exp_(x_k)^(-1)(f(y_(k-1)))+u_k).作为一个应用,给出任意微分同胚在C^0扰动下,如果在双曲集邻域内存在不变集,则其是拓扑拟稳定的. 相似文献
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Bouncing Ball映射的双曲不变集 总被引:1,自引:0,他引:1
对碰撞恢复系数范围为 0 <α<1的“弹跳球 (Bouncing Ball)”映射 ,通过适当的坐标变换 ,给出了双曲不变集存在的严格条件 . 相似文献
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双曲型Lagrangian函数 总被引:12,自引:0,他引:12
双曲复数与Minkowski几何相对应,由四维时空间隔不变量和双曲型Lorentz变换可导出双曲型Lagrangian方程和Hamilton_Jacobi方程· 相似文献
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尹永成 《数学年刊A辑(中文版)》1999,(5)
本文证明了半双曲有理映射Julia集的局部连通性,推广了Carleson-Jones-Yoccoz关于多项式的结果,同时还考虑了半双曲有理映射Julia集的面积问题. 相似文献
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本文证明了Riemann流形上的微分同胚f在其双曲不变集附近具有相对于C1小扰动一致的极限 跟踪性.还证明了如果f是C1-结构稳定的,则,具有极限跟踪性. 相似文献
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本文提出并研究带有线性外力场的双曲平均曲率流,通过凸曲线的支撑函数,导出一个双曲型Monge-Ampère 方程并将其转化成Riemann 不变量满足的拟线性双曲方程组。利用拟线性双曲方程组Cauchy 问题的局部解理论,讨论带有线性外力场的双曲平均曲率流Cauchy 问题经典解的生命跨度(即局部解存在的最大时间区间)。 相似文献
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In this paper we study the possibility of globally stabilizinginvariant sets of autonomous continuous nonlinear systems bythe state (output) feedback control law. We show that the topologicalstructure of invariant sets can give rise to obstruction tothe existence of a continuous control law for global stabilizationof invariant sets. 相似文献
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Konstantin E. Starkov 《Communications in Nonlinear Science & Numerical Simulation》2009,14(6):2565-2570
This paper is concerned with the localization problem of compact invariant sets of the system describing dynamics of the nuclear spin generator. We establish that all compact invariant sets of this system are located in the intersection of a ball with two frusta and compute its parameters. In addition, localization by using the two-parameter set of parabolic cylinders is described. Our results are obtained with help of the iteration theorem concerning a localization of compact invariant sets. One numerical example illustrating a localization of a chaotic attractor is presented as well. 相似文献
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具有变时滞Hopfield型神经网络的正不变集与吸引集 总被引:2,自引:0,他引:2
研究了具有变时滞Hopfield型神经网络的正不变集与吸引集,获得了正不变集与吸引集存在性的充分判据。 相似文献
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L-fuzzy代数的刻画 总被引:4,自引:0,他引:4
鉴于[2]中已有fuzzy代数结合的不理想,谷文祥和卢荼在L-fuzzy集论中重新定义了L-fuzzy代数,得到了一些理想的结论。但却没有给出它的截集式刻画。本文的目的就是借助于L-fuzzy集的几种水平截集给出了它的几个等价刻画,使得它的表现更为直观且更便于应用。最后,作为应用,本文简洁地证明了L-fuzzy代数在代数同态下是不变的和逆不变的。 相似文献
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A. P. Krishchenko 《Differential Equations》2016,52(11):1403-1410
We study the asymptotic stability and the global asymptotic stability of equilibria of autonomous systems of differential equations. We prove necessary and sufficient conditions for the global asymptotic stability of an equilibrium in terms of invariant compact sets and positively invariant sets. To verify these conditions, we use some results of the localization method for invariant compact sets of autonomous systems. These results are related to finding sets that contain all invariant compact sets of the system (localizing sets) and to the behavior of trajectories of the system with respect to localizing sets. We consider an example of a system whose equilibrium belongs to the critical case. 相似文献
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The paper is concerned with negatively invariant sets of local cocycles generated, in particular, by nonautonomous ordinary
differential equations. Upper estimates for the Hausdorff dimension for negatively invariant sets of local cocycles are obtained
using singular numbers of linearization of the cocycle and special functions of Lyapunov type. 相似文献
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The localization problem of compact invariant sets of the Rössler system is considered in this paper. The main interest is attracted to a localization of periodic orbits. We establish a number of algebraic conditions imposed on parameters under which the Rössler system has no compact invariant sets contained in half-spaces z > 0; z < 0 and in some others. We prove that if parameters (a, b, c) of the Rössler system are such that this system has no equilibrium points then it has no periodic orbits as well. In addition, we give localization conditions of compact invariant sets by using linear functions and one quadratic function. 相似文献
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Two-dimensional invariant tori in the neighborhood of an elliptic equilibrium of Hamiltonian systems
In this paper, we prove that a Hamiltonian system possesses either a four-dimensional invaxiant disc or an invariant Cantor set with positive (n + 2)-dimensional Lebesgue measure in the neighborhood of an elliptic equilibrium provided that its lineaxized system at the equilibrium satisfies some small divisor conditions. Both of the invariant sets are foliated by two-dimensional invaxiant tori carrying quasi-oeriodic solutions. 相似文献