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1.
Belov V. V. Dobrokhotov S. Yu. Maksimov V. A. 《Theoretical and Mathematical Physics》2003,135(3):765-791
Different versions of the Darboux–Weinstein theorem guarantee the existence of action–angle-type variables and the harmonic-oscillator variables in a neighborhood of isotropic tori in the phase space. The procedure for constructing these variables is reduced to solving a rather complicated system of partial differential equations. We show that this system can be integrated in quadratures, which permits reducing the problem of constructing these variables to solving a system of quadratic equations. We discuss several applications of this purely geometric fact in problems of classical and quantum mechanics. 相似文献
2.
Junxiang Xu 《Proceedings of the American Mathematical Society》2007,135(3):805-814
In this paper we consider a class of non-conservative dynamical system with small perturbation. By the KAM method we prove existence of Floquet invariant tori under the weakest non-resonant conditions.
3.
CHEN Hongjia GAO Yun & SHANG Shikui Department of Mathematics University of Science Technology of China Hefei China Department of Mathematics Statistics York University Toronto Ontario Canada MJ P 《中国科学A辑(英文版)》2006,(11)
We use a fermionic extension of the bosonic module to obtain a class of B(0, A)graded Lie superalgebras with nontrivial central extensions. 相似文献
4.
We study numerically the complex domains of validity for KAM theory in generalized standard mappings. We compare methods based on Padé approximants and methods based on the study of periodic orbits. 相似文献
5.
We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature orientable surfaces immersed in a Riemannian Killing submersion. As a consequence, the strong stability of such surfaces is studied. We also characterize constant mean curvature Hopf tori as the only ones attaining the bound in certain cases. 相似文献
6.
Sérgio R. Fenley 《Geometriae Dedicata》2003,99(1):61-102
We study incompressible tori in 3-manifolds supporting pseudo-Anosov flows and more generally ZZ subgroups of the fundamental group of such a manifold. If no element in this subgroup can be represented by a closed orbit of the pseudo-Anosov flow, we prove that the flow is topologically conjugate to a suspension of an Anosov diffeomorphism of the torus. In particular it is non singular and is an Anosov flow. It follows that either a pseudo-Anosov flow is topologically conjugate to a suspension Anosov flow, or any immersed incompressible torus can be realized as a free homotopy from a closed orbit of the flow to itself. The key tool is an analysis of group actions on non-Hausdorff trees, also known as R-order trees – we produce an invariant axis in the free action case. An application of these results is the following: suppose the manifold has an R-covered foliation transverse to a pseudo-Anosov flow. If the flow is not an R-covered Anosov flow, then it follows that the manifold is atoroidal. 相似文献
7.
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 .
8.
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
9.
Björn Birnir 《Journal of statistical physics》2007,128(1-2):535-568
A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirók et al. [Phys. Rev. Lett.
75(6):1226–1229, 1995], describing the motion of a school of fish. Classes of linear and stationary solutions of the ODEs are
found and their stability explored using equivariant bifurcation theory. The existence of periodic and toroidal solutions
is also proven under deterministic perturbations and structurally stable heteroclinic connections are found. Applications
of the model to the migration of the capelin, a pelagic fish that undertakes an extensive migration in the North Atlantic,
are discussed and simulation of the ODEs presented. 相似文献
10.
Consider a one-mass system with two degrees of freedom, non-linearly coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable, a stable periodic solution may emerge, there are also cases where the trivial solution is stable and co-exists with a stable periodic solution; if both the trivial solution and the periodic solution(s) are unstable, we find an attracting torus with large amplitudes by a Neimark-Sacker bifurcation. The results of the harmonic balance method and averaging are compared, as well as the results on the Neimark-Sacker bifurcation obtained by the numerical software package CONTENT and by averaging. In all cases we have good agreement. 相似文献