共查询到20条相似文献,搜索用时 78 毫秒
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本文首先用正则摄动方法给出一类含小参数常微分方程组的近似不变流形和近似分析解。然后,给出近似分析解的误差估计式;并且证明了在一定的条件下,这类近似不变流形是中心流形的近似表示式。 相似文献
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本文就弱非线性自治系统,引入了不变流形理论的几何描述,应用稳定流形定理,Lyapunov子中心流形定理以及中心流形定理,给出了非线性模态的定义,存在条件以及模态的轨道特性·采用了近似的级数展开方法确定模态子流形及模态运动·给出的算例是对本文方法的验证和解释· 相似文献
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本文首次提出股票市场价格流形的概念 ,并对由维纳过程 (布朗运动 )驱动的市场价格动态扩散过程模型 (X)的不变流形作了初步的讨论 ,给出了一个判定一个给定的价格流形M是市场模型 (X)的不变流形的充分条件 . 相似文献
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具变号系数的四阶非线性微分方程的振动性 总被引:2,自引:0,他引:2
研究了四阶非线性微分方程x(4)(t)+p(t)f(x(t))=0的振动性,对振动因子p(t)变号的情况,给出了两个重要的引理,并得到方程振动的一个充分性定理.所得结论推广了四阶非线性微分方程当系数不变号时原有的振动性结论. 相似文献
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本文给出了Sasakian流形中反不变极小子流形是稳定或不稳定的一个充分条件. 相似文献
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Bouncing Ball模型的弱混沌性 总被引:1,自引:0,他引:1
用异于传统的方法,作出Bouncing Ball映射不变流形的对称流形,从而成功地将稳定流形与不稳定流形的位置进行比较。应用[1]关于弱横截与弱混沌的有关概念及定理,给出了Borncing Ball映射产生弱混沌的较为一般的参数区域,进一步提示了Bouncing Ball映射的动力学行为。 相似文献
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某类系数变号的二阶非线性变时滞微分方程的振动性 总被引:1,自引:1,他引:0
研究了二阶非线性变时滞微分方程x″(t)+p(t)f(x(g(t)))=0的振动性,对振动因子p(t)变号的情况,给出了两个重要的引理,并得到方程振动的一个充分性定理.所得结论推广了二阶非线性变时滞微分方程当系数不变号时原有的振动性结论. 相似文献
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Malgorzata Guzowska Saber Elaydi 《Journal of Difference Equations and Applications》2013,19(12):1851-1872
In this paper, we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important centre manifolds, and study their bifurcation. Saddle-node and period-doubling bifurcation route to chaos are exhibited via numerical simulations. 相似文献
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In this paper we introduce a concept of exponential dichotomy for linear skew-product semiflows (LSPS) in infinite dimensional Banach spaces, which is an extension of the classical concept of exponential dichotomy for time dependent linear differential equations in Banach spaces. We prove that the concept of exponential dichotomy used by Sacker-Sell and Magalhães in recent years is stronger than this one, but they are equivalent under suitable conditions. Using this concept we where able to find a formula for all the bounded negative continuations. After that, we characterize the stable and unstable subbundles in terms of the boundedness of the corresponding projector along (forward/backward) the LSPS and in terms of the exponential decay of the semiflow. The linear theory presented here provides a foundation for studying the nonlinear theory. Also, this concept can be used to study the existence of exponential dichotomy and the roughness property for LSPS.
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Global stable and unstable manifolds for a class of semilinear equations with sectorially dichotomous operator 下载免费PDF全文
In this paper, the existence and smoothness of global stable and unstable manifolds at an equilibrium are established for a class of semilinear equations with sectorially dichotomous operator. As an application, an elliptic PDE in infinite cylindrical domain is discussed. 相似文献
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Shu Zhu 《中国科学A辑(英文版)》1998,41(2):147-157
A detailed presentation of an unstable manifold theorem for non-invertible differentiable maps of finite-dimensional manifolds
is given. 相似文献
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We construct smooth stable invariant manifolds for a class of delay equations with piecewise constant delay, for any sufficiently small perturbation of a nonuniform exponential dichotomy. We build on former work for perturbations of a uniform exponential dichotomy, also for delay equations with piecewise constant delay. These equations can be described as delay equations with an impulsive behavior of the derivative, such that at certain times the derivative changes abruptly. 相似文献
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本文介绍Lie代数双极化与齐性仿凯勒流形的若干新进展,并提出了若干相关问题,指出该领域可能发展的若干方向。 相似文献
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S. Shekhar 《Journal of Nonlinear Science》1996,6(2):105-138
Summary An application in robotics motivates us to characterize the evolution of a subset in state space due to a compact neighborhood
of an arbitrary dynamical system—an instance of a differential inclusion. Earlier results of Blagodat·skikh and Filippov (1986)
and Butkovskii (1982) characterize the boundary of theattainable set and theforward projection operator of a state. Our first result is a local characterization of the boundary of the forward projection ofa compact regular subset of the state space.
Let the collection of states such that the differential inclusion contains an equilibrium point be called asingular invariant set. We show that the fields at the boundary of the forward projection of a singular invariant set are degenerate under some
regularity assumptions when the state-wise boundary of the differential inclusion is smooth. Consider instead those differential
inclusions such that the state-wise boundary of the problem is a regular convex polytope—a piecewise smooth boundary rather
than smooth. Our second result gives conditions for theuniqueness andexistence of the boundary of the forward projection of a singular invariant set. They characterize the bundle of unstable and stable
manifolds of such a differential inclusion. 相似文献
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S. R. Fenley 《Commentarii Mathematici Helvetici》1998,73(2):259-297
In this article we study the topology of Anosov flows in 3-manifolds. Specifically we consider the lifts to the universal
cover of the stable and unstable foliations and analyze the leaf spaces of these foliations. We completely determine the structure
of the non Hausdorff points in these leaf spaces. There are many consequences: (1) when the leaf spaces are non Hausdorff,
there are closed orbits in the manifold which are freely homotopic, (2) suspension Anosov flows are, up to topological conjugacy,
the only Anosov flows without free homotopies between closed orbits, (3) when there are infinitely many stable leaves (in
the universal cover) which are non separated from each other, then we produce a torus in the manifold which is transverse
to the Anosov flow and therefore is incompressible, (4) we produce non Hausdorff examples in hyperbolic manifolds and derive
important properties of the limit sets of the stable/unstable leaves in the universal cover.
Received: March 13, 1997 相似文献
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Antonio J. Ureña 《Journal of Differential Equations》2007,240(1):172-195
A classical result, studied, among others, by Carathéodory [C. Carathéodory, Calculus of Variations and Partial Differential Equations of the First Order, Chelsea, New York, 1989], states that, for second-order, scalar equations, nondegenerate periodic minimizers are hyperbolic. Consequently, the Stable/Unstable Manifold Theorem applies, and implies that, at least locally, the stable and unstable sets are regular curves intersecting transversally at the nondegenerate minimizer.For analytic equations, there is a version of this fact which holds for isolated, but possibly degenerate, minimizers. 相似文献