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1.
We investigate the orbital diffusion and the stickiness effects in the phase space of a 3-dimensional volume preserving mapping.
We first briefly review the main results about the stickiness effects in 2-dimensional mappings. Then we extend this study
to the 3-dimensional case, studying for the first time the behavior of orbits wandering in the 3-dimensional phase space and
analyzing the role played by the hyperbolic invariant sets during the diffusion process. Our numerical results show that an
orbit initially close to a set of invariant tori stays for very long times around the hyperbolic invariant sets near the tori.
Orbits starting from the vicinity of invariant tori or from hyperbolic invariant sets have the same diffusion rule. These
results indicate that the hyperbolic invariant sets play an essential role in the stickiness effects. The volume of phase
space surrounded by an invariant torus and its variation with respect to the perturbation parameter influences the stickiness
effects as well as the development of the hyperbolic invariant sets. Our calculations show that this volume decreases exponentially
with the perturbation parameter and that it shrinks down with the period very fast. 相似文献
2.
我们已经研究了分别具椭圆和双曲不动点的二维保测度映射及其受摄三维扩张的ＫＳ熵。本文研究一类具抛物不动点的二维保测度映射：及其受摄扩张：的ＫＳ熵随参数Ａ、Ｂ、Ｃ、Ｄ、Ｅ的变化．数值探索结果表明：适当定义区域内的二维映射Ｔ２的ＫＳ熵与Ａ无关，与我们的理论分析结果相一致。受摄扩张映射Ｔ３的ＫＳ熵随摄动参数Ｂ、Ｃ、Ｄ的增大而增大，却随Ｅ的增大而减小．我们还发现，随着摄动的逐渐增强，映射Ｔ３的不变环面将逐渐破裂，使更多的轨道逃逸，从而可能使映射Ｔ３的ＫＳ熵减小。另外，不变环面存在的判别式在大范围内仍在一定程度上有效。 相似文献
3.
A non-linear gravitational model with a multidimensional geometry and quadratic scalar curvature is considered. For certain
parameter ranges, the extra dimensions are stabilized if the internal spaces have negative constant curvature. As a consequence,
the 4-dimensional effective cosmological constant as well as the bulk cosmological constant become negative. The homogeneous
and isotropic external space is asymptotically AdS4. The connection between the D-dimensional and the 4-dimensional fundamental mass scales sets an additional restriction on
the parameters of the considered non-linear models.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
We studied the stability of the restricted circular three-body problem. We introduced a model Hamiltonian in action-angle Delaunay variables. which is nearly-integrable with the perturbing parameter representing the mass ratio of the primaries. We performed a normal form reduction to remove the perturbation in the initial Hamiltonian to higher orders in the perturbing parameter. Next we applied a result on the Nekhoroshev theorem proved by Pöschel [13] to obtain the confinement in phase space of the action variables (related to the elliptic elements of the minor body) for an exponentially long time. As a concrete application. we selected the Sun-Ceres-Jupiter case, obtaining (after the proper normal form reduction) a stability result for a time comparable to the age of the solar system (i.e., 4.9 · 109 years) and for a mass ratio of the primaries less or equal than 10–6. 相似文献
5.
Bruno Cordani 《Celestial Mechanics and Dynamical Astronomy》2000,77(3):185-200
The usual action-angle variables for the Kepler Problem (the Delaunay variables) are not globally defined, leaving out some
orbits (circular orbits or those lying on the xy-plane). Moreover they are trascendental functions of the physical variables, making it quite difficult to write the perturbed
Hamiltonian. The way-out proposed here is to pass to a 8-dimensional rank-6 Poisson manifold, that is, to parametrize the
state of the Kepler Problem with two 4-dimensional vectors mutually orthogonal and of equal norm.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
6.
A coordinate system is defined on the phase space of a perturbed Keplerian system after the mean anomaly has been averaged out, for the purpose of explaining how eliminating the longitude of the ascending node reduces the orbital space to a two-dimensional sphere in case the system admits an axial symmetry. Concomitantly, on the submanifold of direct osculating ellipses, the CDM variables are replaced by functions which form the basis of a Poisson algebra isomorphic to the Lie algebra so(3) of the rotation group SO(3); furthermore, in these variables, the doubly reduced phase flow appears like a rotation of the reduced phase space. 相似文献
7.
重谱即傅立叶空间的三点相关函数，是研究由引力不稳定性产生的大尺度结构的最低非高斯阶统计性质．在傅立叶空间中，发现二维和三维空间的统计性质是等价的，相对三维快速傅立叶，二维快速傅立叶变换可以节省很多计算机资源．结合二维和三维的快速傅立叶变换，利用高精度的初始谱指数为-1的N体数值模拟，测量了从弱线性区域到强非线性区域的重谱．在测量过程中，考虑并严格校正了作用于功率谱和重谱上的数值效应，如离散效应（particle discreteness）、软化因子（force softening）、模拟盒子的大小、混淆效应（alias effect）．发现约化重谱即使在强非线性区域仍然依赖于三角形的形状和尺度，并随着波数的增加而增加，这和前人的假设完全不同．在测量结果的基础上，拟合了重谱的一个适用于初始谱指数为-1的宇宙学模型的经验公式． 相似文献
8.
Pierre Magnenat 《Celestial Mechanics and Dynamical Astronomy》1985,35(4):329-342
Three different numerical techniques are tested to determine the number of integrals of motion in dynamical systems with three degrees of freedom.
- The computation of the whole set of Lyapunov Characteristic Exponents (LCE).
- The triple sections in the configurations space.
- The Stine-Noid box-counting technique.
9.
Relations are established between the Delaunay variables defined over a phase space E in four dimensions and the Lissajous variables defined over a four-dimensional phase space F when the latter is mapped onto E by a parabolic canonical transformation. 相似文献
10.
The exact cosmological vacuum solutions of Brans and Dicke's scalas-tensor theory are derived when a power law is valid between
the gravitational constant κ and the radius of curvatureR of the universe. There exist even in the case of the closed 3-dimensional space of positive curvature solutions with increasingR and κ with respect to the age of the universe, whereby the freely available parameter ω of the scalar-tensor theory can take
all values greater than −3/2. Such solutions are contrary to Dirac's hypothesis as well as to Einstein-Mach's principle. 相似文献
11.
Ch. Skokos G. Contopoulos C. Polymilis 《Celestial Mechanics and Dynamical Astronomy》1996,65(3):223-251
We numerically investigate the projections of non periodic orbits in a 4-dimensional (4-D) symplectic map composed of two coupled 2-dimensional (2-D) maps. We describe in detail the structures that are produced in different planes of projection and we find how the morphology of the 4-D orbits is influenced by the features of the 2-D maps as the coupling parameter increases. We give an empirical law that describes this influence. 相似文献
12.
The phase space of a cosmological model with a scalar field coupled to curvature is discussed in detail for any value of the coupling constant ξ and any power law (ϕ2n) potential. The results obtained generalize previous studies with minimal coupling (ξ = 0) and quadratic or quartic potentials to the entire parameter space (ξ, n). In many cases one finds global attractors and inflationary trajectories, with or without the correct Friedmannian limit. If the coupling constant is positive, a forbidden region cuts out a large part of the phase space, while, if it is negative, escaping regions may occur. Semi-classical instability of vacuum states and singularity-free trajectories are also discussed. 相似文献
13.
The best way to investigate the long-time behaviour of dynamical systems is to introduce an appropriate Poincaré mapping P and study its iterates.Two cases of physical interest arise: Conservative and dissipative systems. While the latter has been considered by a great many authors, much less is known for the first one (according to Liouville's theorem, here the mapping leaves a certain measure in phase space invariant). In this paper, we concentrate our attention on compact phase spaces (or, rather, surfaces of section). This assumption is mathematically useful and physically reasonable.We consider the simplest possible (2-dimensional) systems whehre the phase space is the compact unit disk D in 2. A family of simple area-preserving mappings from D onto itselves will be given and discussed in detail.It is shown that general characteristics of the dynamics are quite similar to those of e.g. the Hénon-Heiles system, while other features, as the structure of invariant curves, are different. 相似文献
14.
《Chinese Astronomy and Astrophysics》2006,30(2):133-149
Bispectrum, or three-point correlation function in Fourier space, is the lowest order non-Gaussian statistic to study the large-scale structure produced by gravitational instability. In Fourier space, the 2-dimensional density field has the same statistical properties as the 3-dimensional field, and compared with the 3-dimensional fast Fourier transform (FFT), the 2-dimensional FFT can save a lot of computer resources. In a combination of 2- and 3-dimensional FFTs and using a high-resolution N-body numerical simulation with the initial spectral index -1, we have measured the bispectrum from the weakly linear regime to the strongly nonlinear regime. All possible effects of numerical artefacts on the power spectrum and bispectrum, such as particle discreteness, force softening, finite box size and alias effect, are considered and strictly corrected. In contrast with what previous researchers assumed, it is revealed that the reduced bispectrum depends on the triangle shape and scale even in the strongly nonlinear regime, and increases with the wave number. And based on the measured results, a new fitting formula for the bispectum suitable for cosmological models with an initial spectral index −1 is obtained. 相似文献
15.
Lars Danielsson 《Astrophysics and Space Science》1969,5(1):53-58
The distribution of asteroid orbits in space is studied and a detailed investigation for Hirayama's Flora family is presented. Some tendencies to (5-dimensional) clustering are found by means of comparing actual with random distribution simulated on a computer. 相似文献
16.
17.
基于NNR-NUVEL-1A地球板块运动模型和ITRF2000地球参考架的三维VLBI站速度矢量,采用实测的VLBI基线长度变化率作为约束,重新估计了部分国际VLBI站的局部或区域性地壳的垂直形变,并与国际地球参考架ITRFs解和VLBI全球解GLB2003,VTRF2003和VTRF2005的结果进行了比较。结果表明,欧亚板块的URUMQI站和太平洋板块的KWAJAL26站,南极OHIGGINS站的垂直形变率、ITRFs解和VLBI全球解存在6-15mm/a的差异,北美YUMA站可能有15-31mm/a 的垂直形变率,而美国西部太平洋板块的San Francisco(PRESIDIO)站的垂直形变率还有待进一步的研究。此外,SC-VLBA,CRIMEA和EFLSBERG站的垂直形变率、ITRFs解和VLBI全球解的差约为1-6mm/a。用不同方法得到的VLBI站的水平形变率解有较好的一致性。 相似文献
18.
《Chinese Astronomy and Astrophysics》2023,47(1):1-53
Coronal mass ejection (CME) is the large scale magnetized plasmoid ejected from the Sun, which brings huge amount of magnetic flux and plasma into interplanetary space. An earthward CME will interact with the magnetosphere of the Earth, and invokes the substorm and the other phenomena of the space weather as it approaches to the Earth. The 2-dimensional data provided by the current observational techniques cannot describe the true magnetic structure and the plasma distribution of CMEs comprehensively. We need to look into the 3-dimensional structure and the associated three components of CME speeds in order to predict the time when an ICME (Interplanetary CME) reaches the Earth, and the potential consequent impact on the Earth and the nearby environment. In this paper, 3D reconstruction methods of CME based on existing imaging observations are introduced, including two kinds of reconstruction methods based on coronagraph data and heliosphere imager data, and CME-driven shock wave 3D reconstruction methods with high correlation with CME imaging reconstruction. Each method shows apparent advantages in dealing with specific events, but its weakness and necessary constrains to its applications exist as well. Results obtained via various methods are compared in this work, and we found that CME velocities and moving directions deduced from these methods are fairly close to one another, which shows high reliability of these methods. Finally, the hot topics related to the 3-dimensional reconstruction of CME (ICME) and the relevant development in reconstructing methods are also discussed. 相似文献
19.
Action-angle variables for the Levi-Civita regularized planar Kepler problem were introduced independently first by Chenciner and then by Deprit and Williams. The latter used explicitly the so-called Lissajous variables. When applied to the transformed Keplerian Hamiltonian, the Lissajous transformation encounters the difficulty of being defined in terms of the constant frequency parameter, whereas the Kepler problem transformed into a harmonic oscillator involves the frequency as a function of an energy-related canonical variable. A simple canonical transformation is proposed as a remedy for this inconvenience. The problem is circumvented by adding to the physical time a correcting term, which occurs to be a generalized Kepler’s equation. Unlike previous versions, the transformation is symplectic in the extended phase space and allows the treatment of time-dependent perturbations. The relation of the extended Lissajous–Levi-Civita variables to the classical Delaunay angles and actions is given, and it turns out to be a straightforward generalization of the results published by Deprit and Williams. 相似文献
20.
The motion of two massive particles is considered within the framework of the first post-Newtonian approximation. The system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables. Closed-form solutions for the Delaunay elements in the phase space are obtained. The bridge between the phase space and the state space of the Lagrangian of the motion is provided by a velocity-dependent Legendre transformation. By explicit inversion of this transformation, expressions for the Keplerian elements in the state space are obtained from the Delaunay element solutions. 相似文献