共查询到20条相似文献,搜索用时 546 毫秒
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George Contopoulos 《Milan Journal of Mathematics》2009,77(1):101-126
We consider the characteristics of order and chaos in dynamical systems, with emphasis on the orbits in astronomical systems.
Celestial mechanics deals with orbits in the solar system, which are mainly ordered. On the other hand the orbits of stars
in galaxies were considered to be chaotic. However numerical experiments have shown that in general a system contains both
ordered and chaotic orbits. Thus a new classification of dynamical systems has been established. We describe ordered and chaotic
orbits in galaxies and in mappings. Some ordered orbits appear even in strongly perturbed systems. The transition from order
to chaos is due to resonance overlapping. Then we describe some recent developments concerning order and chaos in the solar
system and in galaxies. The outer spiral arms in strong barred galaxies are composed mainly of sticky chaotic orbits. Ordered
and chaotic orbits appear also in Bohmian quantum mechanics. If the initial probability p is not equal to the square of the wave function |ψ|2, then in the case of ordered orbits p never approaches |ψ|2, while in the case of chaotic orbits p → |ψ|2 after a time interval called “quantum Nekhoroshev time”. 相似文献
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We consider the nonlinear diffusion-absorption problem in L1() u - div a(, Du) + j (, u) f on , u = 0 on where is an arbitrary open set in N. Conditions for the existence of a strong solution are presented and the existence of a natural generalized solution in the general case is established. We study the dependence of the generalized solution on the absorption term j and characterize generalized solutions which are essentially bounded. 相似文献
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曾云辉 《数学的实践与认识》2010,40(17)
考虑一类具非线性扩散系数的偶数阶中立型阻尼偏微分方程,通过利用广义Riccati变换和引入参数函数,获得了该类方程在Robin边值条件下解振动的充分条件. 相似文献
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The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with
possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version
of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated
by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation
processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in
comparison with most other existing methods of nonlinear filtering. The paper summarizes the main existing results about these
Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated
setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering. 相似文献
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Siberian Mathematical Journal - 相似文献
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WANG Jinhuan TIAN Miaoqing HONG Liang 《偏微分方程(英文版)》2009,22(1):11-31
This paper studies a nonlinear diffusion system with coupled nonlinear boundary flux and two kinds of inner sources (positive for the first and negative for the second), where the four nonlinear mechanisms are described by eight nonlinear parameters. The critical exponent of the system is determined by a complete classification of the eight nonlinear parameters, which is represented via the characteristic algebraic system introduced to the problem. 相似文献
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In this article we have studied the nonlinear interaction between ellipticity and dissipation in a set of model equations (1.1) and established the relation between this interaction and chaos. In addition to theoretical investigations, extensive numerical simulations with these equations have been made, and different routes to chaos have been found. The numerical studies have revealed the chaotic nature of the solutions. 相似文献
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Ya. I. Belopolskaya 《Journal of Mathematical Sciences》2003,118(6):5513-5524
In this paper, we study connections between diffusion processes and some classical equations of mathematical physics and, in particular, of soliton theory. It is shown that some soliton equations correspond to one-parameter families of absolutely continuous transformations of diffusion measures and allow us to derive expressions for the logarithmic derivatives of these measures with respect to parameters. Bibliography: 8 titles. 相似文献
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In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with
structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert
spaces, which generalize the notion of joint block-diagonal mutually incoherent bases introduced by Donoho and Huo. The Bernstein
inequality obtained for such dictionaries is proved to be sharp, but it has an exponent that does not match that of the corresponding
Jackson inequality. 相似文献
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Wu Zhuoqun 《东北数学》1997,(1)
SomePropertiesofSolutionsforaNonlinearDifusionSystem(I)*)WuZhuoqun(伍卓群)andYinJingxue(尹景学)(DepartmemtofMathmatics,JilinUnivers... 相似文献
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Zhong-Hua Yang 《计算数学(英文版)》1989,7(3):262-278
In this paper the results in [5] and [6] related to two-parameter nonlinear problems and computing the folds of degree 3 are generalized to any n-parameter nonlinear problems. Constructing a repeatedly extended system for an n-parameter nonlinear problem we prove that a fold of degree n+1 corresponds to a regular solution of its n-th extended system. Also, the equivalence between the n-th extended system and its reduced system is proved. Finally, some examples are computed. 相似文献