Kuo-Chang Chen

Variational methods on periodic and quasi-periodic solutions for the N-body problem

The purpose of this article is two fold. First, we show how quasi-periodic solutions for the N-body problem can be constructed by variational methods. We illustrate this by constructing uncountably many quasi-periodic solutions for the four- and six-body problems with equal masses. Second, we show by examples that a system of N masses can possess infinitely many simple or multiple choreographic solutions. In particular, it is shown that the four-body problem with equal masses has infinitely many double choreographic solutions and the six-body problem with equal masses has infinitely many simple and double choreographic solutions. Our approach is based on the technique of binary decomposition and some variational properties of Keplerian orbits.

Variational constructions for some satellite orbits in periodic gravitational force fields

In a gravitational force field, a bounded orbit of an infinitesimal point mass is called a satellite orbit. The purpose of this paper is to establish a variational theory for the existence of some relative periodic satellite orbits in periodic gravitational force fields. The gravitation field can be generated by a relative equilibrium or a uniformly rotating asteroid. Our approach is to regard the aggregate of primaries together with the small satellite as a restricted full two-body problem, and then look for direct and retrograde relative periodic satellite orbits by direct methods of calculus of variations. Regularity of the action-minimizing satellite orbit is obtained by providing satisfactory lower bound estimates for the distance between the satellite and the mass center. An upper bound estimate for this distance is also provided as a contrast to classical existence proofs by continuation from infinity.

On the barycenter of the tent map

It is well known that the average position or barycenter of generic orbits for the standard tent map is . Periodic orbits are exceptional orbits in the sense that most of them have barycenters different from . In this paper we prove that for any positive integer , there exist distinct periodic orbits for the standard tent map with the same barycenter. We also provide some patterns of periodic orbits with the same barycenter.

A Theory of Central Measures for Celestial Mechanics

In this paper we create a theory of central measures for celestial mechanics. This theory generalizes central configurations to include continuum mass distributions. Roughly speaking, if

Action-Minimizing Orbits in the Parallelogram Four-Body Problem with Equal Masses

V

Existence and minimizing properties of retrograde orbits to the three-body problem with various choices of masses

is the Newtonian potential generated by a unit point mass, a central measure

Binary Decompositions for Planar N-Body Problems and Symmetric Periodic Solutions

\mu

Symmetry of Positive Solutions of Semilinear Elliptic Equations in Infinite Strip Domains

for

On action-minimizing retrograde and prograde orbits of the three-body problem

V

Removing Collision Singularities from Action Minimizers for the N -Body Problem with Free Boundaries

is a mass distribution in space characterized by the property that gravitational acceleration vector of any