Related papers: Periodic Solutions with Singularities in Two Dimen…
The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…
By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…
Novel classes of dynamical systems are introduced, including many-body problems characterized by nonlinear equations of motion of Newtonian type ("acceleration equals forces") which determine the motion of points in the complex plane. These…
The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…
Analytic methods to investigate periodic orbits in galactic potentials. To evaluate the quality of the approximation of periodic orbits in the logarithmic potential constructed using perturbation theory based on Hamiltonian normal forms.…
The present paper deals with the periodic orbits generated by Lagrangian solutions of the restricted three-body problem when both the primaries are oblate bodies. We have illustrated the periodic orbits for different values of $\mu,…
We present a planar four-body model, called the Binary Asteroid Problem, for the motion of two asteroids (having small but positive masses) moving under the gravitational attraction of each other, and under the gravitational attraction of…
We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the…
We prove the existence of periodic solutions of the N=(n+1)-body problem starting with n bodies whose reduced motion is close to a non-degenerate central configuration and replacing one of them by the center of mass of a pair of bodies…
This dissertation deals with singularity formation in spherically symmetric solutions of the hyperbolic Yang Mills equations in (4+1) dimensions and in spherically symmetric solutions of C P^1 wave maps in (2+1) dimensions. These equations…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite…
Examples are given of solutions of the planar N-body problem which remain the same for at least two systems of masses with the same sum and same center of mass. The least value of N achieved up to now with this property is 474, a number…
We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to…
We consider the restricted n + 1-body problem of Newtonian mechanics. For periodic, planar configurations of n bodies which is symmetric under rotation by a fixed angle, the z-axis is invariant. We consider the effect of placing a massless…
In this paper we investigate the existence of singular solutions to the conformal Dirac-Einstein system. Because of its conformal invariance, there are many similarities with the classical construction of singular solutions for the Yamabe…
This paper concerns the restricted 3-body problem. By applying topological methods we give a computer assisted proof of the existence of some classes of periodic orbits, the existence of symbolic dynamics and we give a rigorous lower…
The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions…
We study central configurations in the four body problem, i.e., configurations in which the forces on all the bodies point to a fixed, single point in space. The newly formulated pair-space formalism yields a set of vectorial equations that…
We investigate a singularly perturbed, non-convex variational problem arising in materials science with a combination of geometrical and numerical methods. Our starting point is a work by Stefan M\"uller, where it is proven that the…