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21.
Frieder Knüppel 《Geometriae Dedicata》1999,76(3):253-264
Let V be a finite-dimensional vector-space. A linear mapping on V is called simple if V( - 1) is 1-dimensional. Let S be a set of simple bijections on V. We discuss conditions entraining that each element of S is orthogonal (respectively symplectic) under an appropriate symmetric (respectively symplectic) bilinear form on V. 相似文献
22.
Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented.
AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett. 相似文献
23.
By a novel approach proposed by Luo, the unconventional Hamilton-type variational principle in phase space for elastodynamics of multidegree-of-freedom system is established in this paper. It not only can fully characterize the initial-value problem of this dynamic, but also has a natural symplectic structure. Based on this variational principle, a symplectic algorithm which is called a symplectic time-subdomain method is proposed. A non-difference scheme is constructed by applying Lagrange interpolation polynomial to the time subdomain. Furthermore, it is also proved that the presented symplectic algorithm is an unconditionally stable one. From the results of the two numerical examples of different types, it can be seen that the accuracy and the computational efficiency of the new method excel obviously those of widely used Wilson-θ and Newmark-β methods. Therefore, this new algorithm is a highly efficient one with better computational performance. 相似文献
24.
Hui Li 《Proceedings of the American Mathematical Society》2003,131(11):3579-3582
Let be a connected, compact symplectic manifold equipped with a Hamiltonian action. We prove that, as fundamental groups of topological spaces, , where is the symplectic quotient at any value in the image of the moment map .
25.
1. PreliminaryIt is well known that{1] a 8ymPlectic form is invariant along the trajectory of a Hamilto-nian system. Based on this fundamental property, certain techniques have been developed.The purpose of this paper is to extend such an approach to a wider class of dynamic systeIns,namely, genera1ized Hamiltonian systems. Our purpose is to investigate a class of dynaInicsystems, which possess a certain "geometric structure".Deflnition 1.1[1'2]. Let M be a tIlallifo1d. w E fl'(M) is call… 相似文献
26.
Paolo Lisca 《Proceedings of the American Mathematical Society》2001,129(11):3437-3444
Let be a closed, oriented -manifold. The set of homotopy classes of positive, fillable contact structures on is a subtle invariant of , known to always be a finite set. In this paper we study under the assumption that carries metrics with positive scalar curvature. Using Seiberg-Witten gauge theory, we prove that two positive, fillable contact structures on are homotopic if and only if they are homotopic on the complement of a point. This implies that the cardinality of is bounded above by the order of the torsion subgroup of . Using explicit examples we show that without the geometric assumption on such a bound can be arbitrarily far from holding.
27.
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
28.
Let X be a Riemann surface equipped with a projective structure. Let
be a square-root of the holomorphic cotangent bundle K
X
. Consider the symplectic form on the complement of the zero section of
obtained by pulling back the symplectic form on K
X
using the map 2. We show that this symplectic form admits a natural quantization. This quantization also gives a quantization of the complement of the zero section in K
X
equipped with the natural symplectic form. 相似文献
29.
本文采用辛算法数值求解一维含时Gross-Pitaevskii(GP)方程.研究了存在陷俘势和撤掉陷俘势时两个凝聚体间的相互作用.发现当存在陷俘势时两个凝聚体间发生弹性碰撞;在零时刻撤掉陷俘势时两个凝聚体间发生干涉现象;当t=2时撤掉陷俘势两个凝聚体间发生了复杂现象. 相似文献
30.
N. A. Tyurin 《Mathematical Notes》1999,65(3):351-357
Three remarks concerning the constructive properties of smooth 4-manifolds with nontrivial Seiberg-Witten invariants are presented.
Translated fromMatematicheskie Zametki, Vol. 65, No. 3, pp. 420–428, March, 1999. 相似文献