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31.
D. Beigie 《Journal of Nonlinear Science》1995,5(1):57-103
Summary We study separatrix crossing in near-integrablek-degree-of-freedom Hamiltonian flows, 2 <k < , whose unperturbed phase portraits contain separatrices inn degrees of freedom, 1 <n <k. Each of the unperturbed separatrices can be recast as a codimension-one separatrix in the 2k-dimensional phase space, and the collection of these separatrices takes on a variety of geometrical possibilities in the reduced representation of a Poincaré section on the energy surface. In general 0 l n of the separatrices will be available to the Poincaré section, and each separatrix may be completely isolated from all other separatrices or intersect transversely with one or more of the other available separatrices. For completely isolated separatrices, transitions across broken separatrices are described for each separatrix by the single-separatrix crossing theory of Wiggins, as modified by Beigie. For intersecting separatrices, a possible violation of a normal hyperbolicity condition complicates the analysis by preventing the use of a persistence and smoothness theory for compact normally hyperbolic invariant manifolds and their local stable and unstable manifolds. For certain classes of multi-degree-of-freedom flows, however, a local persistence and smoothness result is straightforward, and we study the global implications of such a local result. In particular, we find codimension-one partial barriers and turnstile boundaries associated with each partially destroyed separatrix. From the collection of partial barriers and turnstiles follows a rich phase space partitioning and transport formalism to describe the dynamics amongst the various degrees of freedom. A generalization of Wiggins' higher-dimensional Melnikov theory to codimension-one surfaces in the multi-separatrix case allows one to uncover invariant manifold geometry. In the context of this perturbative analysis and detailed numerical computations, we study invariant manifold geometry, phase space partitioning, and phase space transport, with particular attention payed to the role of a vanishing frequency in the limit approaching the intersection of the partially destroyed separatrices. The class of flows under consideration includes flows of basic physical relevance, such as those describing scattering phenomena. The analysis is illustrated in the context of a detailed study of a 3-degree-of-freedom scattering problem. 相似文献
32.
In this paper we construct a family of compact flat manifolds, for all dimensions , with holonomy group isomorphic to and first Betti number zero.
33.
Takashi Koda 《Annals of Global Analysis and Geometry》1993,11(4):323-329
Bérard-Bergery has constructed a non-Kähler Einstein Hermitian metricg with positive scalar curvature on
. We prove thatg is a weakly *-Einstein metric with nonconstant positive *-scalar curvature.This research is partially supported by the Grand-in-Aid for Scientific Research (No. 03740022), the Ministry of Education, Science and Culture. 相似文献
34.
The antisymmetrized geminal power (AGP) and sequential product of geminals(SPG) functions, the basis functions with symplectic symmetry, are linearly combined to calculate the ground state of the LiH molecule. The calculation results show that the AGP or SPG function gives the same ground state results as the linear combination. 相似文献
35.
A toric origami manifold, introduced by Cannas da Silva, Guillemin and Pires,
is a generalization of a toric symplectic manifold. For a toric symplectic manifold, its
equivariant Chern classes can be described in terms of the corresponding Delzant polytope
and the stabilization of its tangent bundle splits as a direct sum of complex line bundles.
But in general a toric origami manifold is not simply connected, so the algebraic topology
of a toric origami manifold is more difficult than a toric symplectic manifold. In this paper
they give an explicit formula of the equivariant Chern classes of an oriented toric origami
manifold in terms of the corresponding origami template. Furthermore, they prove the
stabilization of the tangent bundle of an oriented toric origami manifold also splits as a
direct sum of complex line bundles. 相似文献
36.
37.
In this paper, we study conharmonic curvature tensor in Kenmotsu manifolds with respect to semi-symmetric metric connection and also characterize conharmonically flat, conharmonically semi-symmetric and φ-conharmonically flat Kenmotsu manifolds with respect to semi-symmetric metric connection. 相似文献
38.
Elisa Maria Alessi Gerard GómezJosep J. Masdemont 《Communications in Nonlinear Science & Numerical Simulation》2012,17(2):854-866
We extend the analysis, started in a previous work [1], concerning the formation of lunar impact craters due to low-energy trajectories. First, we adopt the Circular Restricted Three-Body Problem and consider different choices of initial conditions inside the stable invariant manifold associated with the central invariant one in the neighborhood of the L2 equilibrium point in the Earth-Moon system. Then we move to the Bicircular Restricted Four-Body Problem to study the effect of the Sun on the distribution of impacts on the Moon’s surface. 相似文献
39.
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold setting. 相似文献
40.
For a closed symplectic manifold with compatible Riemannian metric g we study the Sobolev geometry of the group of all diffeomorphisms on M which preserve the symplectic structure. We show that, for sufficiently large s, the metric admits globally defined geodesics and the corresponding exponential map is a non-linear Fredholm map of index zero. Finally, we show that the metric carries conjugate points via some simple examples. 相似文献