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21.
HAN Mao''''an & CHEN Xianfeng Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Shanghai Jiao Tong University Shanghai China 《中国科学A辑(英文版)》2005,48(7):940-957
In this paper a bifurcation theorem on the existence of integral manifolds is obtained by using contracting principle. As an application, sufficient conditions for a higher dimensional system to have an integral manifold are given. Especially the existence and uniqueness of a 3-dimensional invariant torus appearing in a 4-dimensional autonomous system with singularity of codimension two are proved. 相似文献
22.
Eugene Lerman Susan Tolman 《Transactions of the American Mathematical Society》1997,349(10):4201-4230
In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly, we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half, we prove that compact symplectic orbifolds with completely integrable torus actions are classified by convex simple rational polytopes with a positive integer attached to each open facet and that all such orbifolds are algebraic toric varieties.
23.
一类量子环面李代数的自同构群 总被引:3,自引:0,他引:3
=C_q[x_1~(±1),x_2~(±1)]为复数域上的非交换环面结合代数,A=\C,Der为的导子李代数.本文研究李代数L_q=DerA的自同构群Aut L_q. 相似文献
24.
Haru T. Pinson 《Journal of statistical physics》1994,75(5-6):1167-1177
We compute the various crossing probabilities defined by R. Langlands, P. Pouliot, and Y. Saint-Aubin for the critical percolation on the torus. 相似文献
25.
A general theory for the study of degenerate Hopf bifurcation in the presence of symmetry has been carried out only in situations where the normal form equations decouple into phase/amplitude equations. In this paper we prove a theorem showing that in general we expect such degeneracies to lead to secondary torus bifurcations. We then apply this theorem to the case of degenerate Hopf bifurcation with triangular (D3) symmetry, proving that in codimension two there exist regions of parameter space where two branches of asymptotically stable 2-tori coexist but where no stable periodic solutions are present. Although this study does not lead to a theory for degenerate Hopf bifurcations in the presence of symmetry, it does present examples that would have to be accounted for by any such general theory. 相似文献
26.
甘春标 《Acta Mechanica Sinica》2004,20(5):558-566
A new procedure is developed to study the stochastic Hopf bifurcation in quasiintegrable-Hamiltonian systems under the Gaussian white noise excitation. Firstly, the singular boundaries of the first-class and their asymptotic stable conditions in probability are given for the averaged Ito differential equations about all the sub-system‘s energy levels with respect to the stochastic averaging method. Secondly, the stochastic Hopf bifurcation for the coupled sub-systems are discussed by defining a suitable bounded torus region in the space of the energy levels and employing the theory of the torus region when the singular boundaries turn into the unstable ones. Lastly, a quasi-integrable-Hamiltonian system with two degrees of freedom is studied in detail to illustrate the above procedure.Moreover, simulations by the Monte-Carlo method are performed for the illustrative example to verify the proposed procedure. It is shown that the attenuation motions and the stochastic Hopf bifurcation of two oscillators and the stochastic Hopf bifurcation of a single oscillator may occur in the system for some system‘s parameters. Therefore, one can see that the numerical results are consistent with the theoretical predictions. 相似文献
27.
The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincare map, the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus. Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied. The Melnikov‘s global perturbation technique was therefore generalized to higher dimensional systems. The region in parameter space where chaotic dynamics may occur was given. It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur. 相似文献
28.
参数激励耦合系统的复杂动力学行为分析 总被引:3,自引:0,他引:3
分析了耦合van der Pol振子参数共振条件下的复杂动力学行为.基于平均方程,得到了参数平面上的转迁集,这些转迁集将参数平面划分为不同的区域,在各个不同的区域对应于系统不同的解.随着参数的变化,从平衡点分岔出两类不同的周期解,根据不同的分岔特性,这两类周期解失稳后,将产生概周期解或3—D环面解,它们都会随参数的变化进一步导致混吨.发现在系统的混沌区域中,其混吨吸引子随参数的变化会突然发生变化,分解为两个对称的混吨吸引子.值得注意的是,系统首先是由于2—D环面解破裂产生混吨,该混吨吸引子破裂后演变为新的混吨吸引子,却由倒倍周期分岔走向3—D环面解,也即存在两条通向混沌的道路:倍周期分岔和环面破裂,而这两种道路产生的混吨吸引子在一定参数条件下会相互转换. 相似文献
29.
Analytic Hardy and BMO spaces on the quantum torus are introduced. Some basic properties of these spaces are presented. In particular, the associated H 1-BMO duality theorem is proved. Finally, we discuss some possible extensions of the obtained results. 相似文献
30.
The amoeba of a complex curve in the 2‐dimensional complex torus is its image under the projection onto the real parts of the logarithmic coordinates. A toric cycle in the complement to a curve is a fiber of this projection over a point in the complement to the amoeba of the curve. We consider amoebas of complex algebraic curves defined by so‐called Harnack polynomials. We prove that toric cycles are homologically independent in the complement to a such curve. 相似文献