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31.
LI Xiong 《数学年刊B辑(英文版)》2001,22(1):31-46
51. IntroductionThe boundedness problem of solutions of the following nonlinear scalar differelltial equa-nons of second order..x f(x, t)ic g(x, t) = 0 (1'1)has been widely investigated by many authors since the 1940's, where f(x, t 1) = j(x, t),g(x, t 1) = g(x, t).When j(x, t) = 0, Equation (1.1) is a conservative system and takes the following form..x g(x, t) ~ 0. (1'2)The first contribution of the boundedness of all the solutions of Equation (1.2) is due toMorrislll, whO proved … 相似文献
32.
In this paper we prove the persistence of lower-dimensional invariant tori of integrable equations after Hamiltonian perturbations under the first Melnikov's non-resonance condition. The proof is based on an improved KAM machinery which works for the angle variable dependent normal form. By an example, we also show the necessity of the Melnikov's first non-resonance condition for the persistence of lower dimensional tori. 相似文献
33.
Tanya Schmah 《Proceedings of the American Mathematical Society》2001,129(4):1169-1177
Which -dimensional orbi-spaces have effective symplectic - torus actions? As shown by Lerman and Tolman (1997) and Watson (1997), this question reduces to that of characterizing the finite subgroups of centralizers of tori in the real symplectic group . We resolve this question, and generalize our method to a calculation of the centralizers of all tori in .
34.
We consider a pendulum type equation with p-Laplacian , where and p(t) are 1-periodic about every variable. The solutions of this equation present two interesting behaviors. On the one hand, by applying Moser's twist theorem, we find infinitely many invariant tori whenever which yields the bounded-ness of all solutions and the existence of quasi-periodic solutions starting at t = 0 on the invariant tori. On the other hand, if p(t) = 0 and has some specific forms, we find a full symbolic dynamical system made by solutions which oscillate between any two different trivial solutions of the equation. Such chaotic solutions stay close to the trivial solutions in some fixed intervals, according to any prescribed coin-tossing sequence. 相似文献
35.
讨论一类三维系统在周期扰动下的分支问题.假设此三维系统有一族闭轨,利用 Poincar\'e映射及积分流形定理,得到了在周期扰动下由这族闭轨产生次调和解和不变环面的条件,并讨论了次调和解的鞍结点分支. 相似文献
36.
Zai-jiu Shang 《Journal of Dynamics and Differential Equations》2000,12(2):357-383
The mapping version of Pöschel's theory on differentiable foliation structures of invariant tori is presented and the relevant estimates explicitly in terms of the diophantine constant and the nondegeneracy parameters of frequency maps are given. As a direct application of the main result, a generalization of Moser's small twist theorem to high dimensions is given. 相似文献
37.
Chong-Qing Cheng 《Transactions of the American Mathematical Society》2005,357(12):5067-5095
Consider a real analytical Hamiltonian system of KAM type that has degrees of freedom (2$">) and is positive definite in . Let . In this paper we show that for most rotation vectors in , in the sense of ()-dimensional Lebesgue measure, there is at least one ()-dimensional invariant torus. These tori are the support of corresponding minimal measures. The Lebesgue measure estimate on this set is uniformly valid for any perturbation.
38.
Xiong Li 《Proceedings of the American Mathematical Society》2004,132(7):2057-2066
In this paper we will study the boundedness of all solutions for second-order differential equations
where and satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.
where and satisfies the sublinear growth condition. Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible mappings. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.
39.
Yu. S. Kolesov 《Mathematical Notes》1997,62(5):623-628
For a number of meaningful examples, nonresonant wave-type equations are shown to be characterized by periodic dynamics.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 744–750, November, 1997.
Translated by O. V. Sipacheva 相似文献
40.
In this paper, we give weak regularity theorems on P of u~ε(x, P), where u~ε(x, P)is the viscosity solution of the cell problem H_ε(P D_xu~ε, x)=H_ε(P). 相似文献