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81.
I discuss an illustration of a mechanism for Arnolds diffusion following a non-variational approach, and an improvement of the related estimates for the diffusion time. 相似文献
82.
Fabian J. Theis 《Mathematische Nachrichten》2002,241(1):170-186
Benedetti and Petronio developed in [1] a so called o–Graph Calculus, where a compact oriented 3–manifold with nonempty boundary could be described by a quadrivalent graph together with some extra structure. In this paper, we will show how topological constructions such as puncturing, connected sums, attaching handles, closing boundary components and product and mapping tori constructions can be translated into the o–graph calculus. 相似文献
83.
Abstract In this paper classical nonlinear dynamics approaches are used to study the intense field stabilization (IFS) for ID model atom according to differential equation (DE) and map approximation (MA). The exact stability boundary and region of I-period fixed points in the parameter space of field strength and frequency are obtained, and the results of MA are in excellent agreement with those of DE. The electrons dynamical behavior in phase space is investigated and the IFS mainly occurring in high frequency regime is confirmed. The stabilization phenomenon connected with the stable fixed points is also examined. In particular it is shown that this phenomenon depends on tightly the KAM tori. It can be predicted that the stabilization probability is just the fraction of initial electrons confined by the KAM tori. 相似文献
84.
Invariant tori in nonlinear oscillations 总被引:2,自引:0,他引:2
The boundedness of all the solutions for semilinear Duffing equationx″ + ω2
x + φ(x) =p(t), ω ∈ ℝ+ℕ is proved, wherep (t) is a smooth 2π-periodic function and the perturbation ⌽(x) is bounded. 相似文献
85.
We show that finitely differentiable diffeomorphisms which are either symplectic, volume-preserving, or contact can be approximated with analytic diffeomorphisms that are, respectively, symplectic, volume-preserving or contact. We prove that the approximating functions are uniformly bounded on some complex domains and that the rate of convergence, in Cr-norms, of the approximation can be estimated in terms of the size of such complex domains and the order of differentiability of the approximated function. As an application to this result, we give a proof of the existence, the local uniqueness and the bootstrap of regularity of KAM tori for finitely differentiable symplectic maps. The symplectic maps considered here are not assumed either to be written in action-angle variables or to be perturbations of integrable systems. Our main assumption is the existence of a finitely differentiable parameterization of a maximal dimensional torus that satisfies a non-degeneracy condition and that is approximately invariant. The symplectic, volume-preserving and contact forms are assumed to be analytic. 相似文献
86.
Zhi Guo WANG 《数学学报(英文版)》2007,23(7):1199-1216
We consider perturbations of integrable Hamiltonian systems in the neighborhood of normally parabolic invariant tori. Using the techniques of KAM-theory we prove that there exists a canonical transformation that puts the Hamiltonian in normal form up to a remainder of weighted order 2d + 1. And some dynamical consequences are obtained. 相似文献
87.
THE KAM THEORY OF DOUBLE PENDULUM 总被引:4,自引:0,他引:4
1EquationofMotionFig.1DoublePendulumConsiderthemotionofadoublependulumPg,whichhastwodegreesoffredomasshowninFig.1.Here,thesu... 相似文献
88.
Zhang Zhengyu 《Annals of Differential Equations》2005,21(4):629-638
Reversible system following Hamiltonian system turns out to be another type of equation which has aroused wide interest in recent years. One open problem is whether the celebrated KAM theory and Nekhoroshev method can be extended to reversible system. As showed in [5], there exist KAM tori in reversible system. In this paper, we give a preliminary discussion on whether there is Nekhoroshev type result in reversible system. In particular, we try to apply this method to the reducibility of a type of common reversible system. 相似文献
89.
Mircea V. Diudea 《Journal of mathematical chemistry》2009,45(2):309-315
The newly proposed Omega counting polynomial is investigated in case of twisted/chiral polyhex tori. Basic definition and
properties are given. A factorization procedure is proposed for finding analytical relationships in families of polyhex toroidal
nanostructures. Numerical data are also given.
Dedicated to Professor Haruo Hosoya, Ochanomizu University, Tokyo, Japan, for his bright contribution to Chemical Graph Theory. 相似文献
90.
We give a nonlinear symplectic coordinator transformation, which can move the normal frequencies of the lower dimensional
torus up to (k,w) where ω is the frequency vector of the torus. That means the normal frequencies with a difference (k,w)
may be regarded as the same. As an application, we derive a persistence result on lower dimensional tori of nearly integrable
Hamiltonian systems when the second Melnikov’s condition is partially violated. 相似文献