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2020年天体力学研讨会

作者:   时间:2020-12-03   点击数:

 

2020年天体力学研讨会程序册

 

主办单位:山东大学数学学院

   间:2020125日至6

会议地点:山东大学中心校区知新楼B924

腾讯会议 ID78649986765

会议密码:1234

 

    组织委员会

    陈国璋   清华大学(台湾)    kchen@math.nthu.edu.tw

    傅燕宁   紫金山天文台            fyn@pmo.ac.cn

    胡锡俊   山东大学                    xjhu@sdu.edu.cn

    孙善忠   首都师范大学            sunsz@cnu.edu.cn

 

    联系人

    胡锡俊   山东大学         xjhu@sdu.edu.cn

    徐梦瑞   山东大学         xumr@mail.sdu.edu.cn

    唐秀婷   山东大学         fztxt@126.com

 

会议日程

2020125

8:50-9:00

开幕式

报告时间

主持人

报告人

报告题目

9:00-9:45

陈国璋

夏志宏

Effective mass and rotational velocity of galaxies

9:50-10:35

严夺魁

Geometric properties of minimizers in the three-body problem

10:35-10:55

休息

10:55-11:40

傅燕宁

许谷榕

The collision singularity of the Kepler problem with singular perturbations

12:00-1:00

午餐

2:00-2:45

严夺魁

张建路

周期性阻尼方程的粘性解参数化及应用

2:50-3:35

尤鹏

Monodromy of Complexified Planar Kepler Problem

3:35-3:55

休息

3:55-4:40

张建路

刘四明 

From period to quasiperiod to chaos: A continuous spectrum of orbits of charged particles trapped in a dipole magnetic field

4:45-5:30

赵磊

Projective Dynamics and an integrable Billiard System of Boltzmann-Gallavotti-Jauslin

2020126

9:00-9:45

孙善忠

孟国武

约旦代数与开普勒问题

9:50-10:35

黎健

The dynamics of Planet 9 on the orbit with large eccentricity and inclination

10:35-10:55

休息

10:55-11:40

黎健

余国巍

Chazy-Type Asymptotics and Hyperbolic Scattering for the n-Body Problem

12:00-1:00

午餐

2:00-2:45

胡锡俊

邢钦

Morse index and stability of the planar N-vortex problem

2:50-3:35

刘博文

Linear stability of elliptic relative equilibria of restricted four-body problem via Maslov index theory

3:35-3:55

休息

3:55-4:40

余国巍

欧昱伟

Linear stability of some elliptic relative equilibria in planar N-body problem

 

报告摘要

报告人:黎健  ljian@nju.edu.cn 南京大学

题目:The dynamics of Planet 9 on the orbit with large eccentricity and inclination 

摘要:当前的Kuiper带小天体,在250个天文单位以外的呈现出奇特的轨道分布特征(如近日点的聚集),基于此,人们猜测在400-800个天文单位的区域内存在所谓9行星。与太阳系8大行星的近圆、几乎共面的轨道不同的是,第9行星可能有着很大的轨道偏心率(e=0.2-0.6)和很高的轨道倾角(i=15-30度)。我们将介绍如何在传统摄动理论的基础上,考虑对大偏心率、高倾角行星轨道的处理,并继而讨论相关的动力学,如在其长期摄动下小天体特殊的轨道分布。

 

报告人:刘博文  bowen.liu@sjtu.edu.cn 上海交大

题目:Linear stability of elliptic relative equilibria of restricted four-body problem via Maslov index Theory

摘要:The N-body problem is one classical topic in dynamical system. In the N-body problem, the periodic solutions which can be written down are so rare when $N$ is greater than 3. The elliptic relative equilibria are among them. The system is called the restricted four-body problem if there are three primaries and one zero-mass body. In this talk, I will introduce elliptic relative equilibria of restricted four-body problem and discuss our recent results on their linear stability via the Maslov index theory. This is a joint work with Prof. Qinglong Zhou.

 

报告人:刘四明  liusm@pmo.ac.cn  紫金山天文台

题目:From period to quasiperiod to chaos: A continuous spectrum of orbits of charged particles trapped in a dipole magnetic field

摘要:It is well-known that there are quasiperiodic orbits around stable periodic orbits in Hamiltonian systems with two degrees of freedom, and these quasiperiodic orbits are stable as well. Since periodic orbits appear to have a negligible measure in the phase space, they are difficult to realize in nature. Quasiperiodic orbits, on the other hand, may occupy a finite volume in the four-dimensional (4D) phase space and be readily detectable. A chaotic orbit has at least one positive Lyapunov exponent. The Lyapunov exponents of quasiperiodic orbits, on the other hand should be zero. Via calculation of the Lyapunov exponent of orbits of trapped charged particles in a dipole magnetic field, we scanned the corresponding phase space and found several prominent regimes of quasiperiodic orbits associated with stable periodic orbits in the equatorial plane. These regimes appear to be connected to some small regimes of quasiperiodic orbits associated with stable periodic orbits in the meridian plane. Our numerical results also show a continuous spectrum of these orbits from stable periodic to quasiperiodic with vanishing Lyapunov exponents and eventually to chaotic ones with at least one positive Lyapunov exponent, and there are unstable periodic orbits with a positive maximum Lyapunov exponent.

 

报告人:孟国武  mameng@ust.hk  香港科技大学

题目:约旦代数与开普勒问题

摘要:开普勒问题是关于太阳系或原子的一个既相当精确又非常简单的物理模型。这个报告的主要目的是想传递两条信息: 1)开普勒问题的数学本质来自约旦代数, 2)开普勒问题对基础物理的决定性影响可能还没有结束。

 

报告人:欧昱伟   ouyw3@mail.sysu.edu.cn  中山大学

题目:Linear stability of some elliptic relative equilibria in planar N-body problem

摘要:In this talk, we study the linear stability of some elliptic relative equilibria in the Planar N-body problem, which include the Lagrangian solution, Euler solution and the (1+n)- gon solution. We will introduce some background, known results and recent progress on this problem.

 

报告人:夏志宏 xia@math.northwestern.edu 美国西北大学

题目:Effective mass and rotational velocity of galaxies

摘要: The rotational velocity of a star in a galaxy is determined by the forces exerted on by other celestial bodies. In a complicated system, the forces may not be easy to compute. We introduce a simple concept of “effective mass” and compute the effective mass in various models. It may provide some additional quantitative analysis on dark matters, if they do exist.

 

报告人:邢钦  xingqin@mail.sdu.edu.cn  山东大学

题目:Morse index and stability of the planar N-vortex problem

摘要:In this talk, I will report some recent results on the stability properties of relative equilibria which are called vortex crystals in the N-vortex problem. Such a configuration can be characterized as critical point of the Hamiltonian function restricted on the constant angular impulse hyper-surface in the phase space. Relative equilibria are generated by the circle action on the so-called shape pseudo-sphere (which generalize the standard shape sphere appearing in the study of the N-body problem). Inspired by the planar N-body problem, and after a geometrical and dynamical discussion of the problem, we investigate the relation intertwining the stability of relative equilibria and the inertia indices of the central configurations generating such equilibria. This is a joint work with Professor Xijun Hu and Professor Alessandro Portaluri.

 

报告人:许谷榕 s9921803@m99.nthu.edu.tw  山东大学

题目:The collision singularity of the Kepler problem with singular perturbations

摘要:We consider the perturbed Kepler problem with singular perturbations, and find conditions under which ejection orbits satisfy the classical Sundman-Sperling estimates. Our argument is based on repeated applications of a second-order differential inequality for boundary value problems. We also show numerical examples of near-collision orbits for several singularly perturbed Kepler problems.

 

报告人:严夺魁  duokuiyan@buaa.edu.cn  北航

题目:Geometric properties of minimizers in the three-body problem

摘要:It is known that each lobe of the famous figure-eight orbit is star-shaped, which implies the polar angle is monotone in each lobe. In general, it is not clear if a trajectory in a minimizer is star-shaped or not. In this talk, we study minimizers connecting two fixed-ends (i.e. the Bolza problem) in the planar three body problem with two equal masses. Actually, we can show that if the fixed ends are both isosceles, the polar angles of their Jacobi coordinates are monotone. This is a joint work with Wentian Kuang. 

 

报告人:尤鹏  you-peng@163.com  首都师范大学

题目:Monodromy of Complexified Planar Kepler Problem

摘要:The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy.

 

报告人:余国巍  yugw@nankai.edu.cn  南开大学陈省身数学研究所

题目:Chazy-Type Asymptotics and Hyperbolic Scattering for the n-Body Problem

摘要:We study solutions of the Newtonian n-body problem which tend to infinity hyperbolically, that is, all mutual distances tend to infinity with nonzero speed as time goes to infinity.  In suitable coordinates, such solutions form the stable or unstable manifolds of normally hyperbolic equilibrium points in a boundary manifold at infinity.  We show that the flow near these manifolds can be analytically linearized and use this to give a new proof of Chazy's classical asymptotic formulas. We also address the scattering problem, namely, for solutions which are hyperbolic in both forward and backward time, how are the limiting equilibrium points related?  After proving some basic theorems about this scattering relation, we use perturbations of our manifold at infinity to study scattering near infinity, that is, when the bodies stay far apart and interact only weakly. This is a joint work with Duignan, Moeckel and Montgomery.

 

报告人:张建路  jzhang87@amss.ac.cn  中科院数学与系统科学研究院

题目:周期性阻尼方程的粘性解参数化及应用

摘要:对于一类在物理,生物以及天文中有广泛应用的周期阻尼方程,我们得到了匹配的Aubry Mather理论并利用粘性解的参数化,揭示在实际问题中的若干变分结论。这一报告基于与严军、王亚南的合作成果。

 

报告人:赵磊  lei.zhao@math.uni-augsburg.de  德国奥格斯堡大学

题目:Projective Dynamics and an integrable Billiard System of Boltzmann-Gallavotti-Jauslin

摘要:A billiard model in a half plane, with the boundary line of the half plane as wall of reflection, defined via the planar Kepler problem, which can be viewed as a limiting case of a more complicated model proprosed by Boltzmann to illustrate his "ergodic hypothesis", is recently shown to be integrable by Gallavotti and Jauslin who explicitely constructed an independent integral additional to the energy. The bounded dynamics of the system has been shown by Felder to carry periodic and quasi-periodic dynamics. In this talk, I shall explain that the integral of Gallavotti-Jauslin is untimately related to the energy of an associated Kepler problem on the sphere. The approach is based on the projective dynamical properties of the Kepler problem. As an additional consequence, we define a class of integrable billiard systems on the sphere with the spherical Kepler problem and with a circle on the sphere as wall of reflection.

 

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