Untitled Document

Special Session 59

Central configurations, periodic solutions, variational method and beyond in celestial mechanics

Organizer(s):

Tiancheng Ouyang

Introduction:

This special session will concentrate on the latest developments in the field of celestial mechanics. In classical celestial mechanics, the motion of the planets and stars is governed by universal gravity and it is mathematically formulated as a second-order system of differential equations, known as the N-body problem. One of the most important types of solutions to the N-body problem is periodic in nature. Among this class of solutions, analyzing the structure and stability of simple, rigidly rotating orbits known as relative equilibria (or central configurations) leads to a greater understanding of the complexities in the full problem. The study of the N-body problem continues to attract researchers in a wide range of fields including dynamical systems, topology, variational methods, algebraic geometry and numerical methods. Much progress has been made recently in the study of the finiteness and stability questions in the N-body problem. This special session provides a marketplace for ideas, and helps identify trends and areas of new opportunity in the field. The session brings established researchers and recent Ph. D graduates together, some of whom are women or from groups underrepresented in mathematics. Some specific topics to be covered include central configurations, discovery of new periodic solutions, variational methods, regularization of collisions, absence of collisions, stability of periodic solutions, spacecraft orbital design and applications of Morse index and Maslov index to the N-body problem. If the schedule permits, we anticipate ending the session with a discussion on open problems.

List of abstracts Go Back
Name	Country	Title
Duokui Yan	Peoples Rep of China	Classification of periodic orbits in the planar four-body problem
Andres Mauricio Rivera Acevedo	Colombia	Bifurcations of periodic solutions from the center of mass in the Generalized Sitnikov (N+1)-body problem
Mitsuru Shibayama	Japan	Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities
Gabriella Pinzari	Italy	Symmetries and reductions in many--body problems
Daniel C Offin	Canada	A variational principle for elliptic stable orbits in low dimensional Hamiltonian systems
Gareth E Roberts	USA	On the Uniqueness of the Regular N-gon Central Configuration
Elizabeth Zolllinger	USA	A family of orbits in the equal mass 3-body problem
Li Bingyu	Peoples Rep of China	Mountain Pass Lemma and New Periodic Solutions of the Singular Second Order Hamiltonian System
Alain Albouy	France	Lower and upper bounds on the number of planar central configurations
Tiancheng Ouyang	USA	Variational method on N-body problem of Celestial Mechanics
Daniel Nunez	Colombia	Quantifying the bifurcation of stable symmetric periodic solutions from the center mass in the Sitnikov Problem