Related papers: Symplectic Regularization of Binary Collisions in …
The existence of elliptic periodic solutions of a perturbed Kepler problem is proved. The equations are in the plane and the perturbation depends periodically on time. The proof is based on a local description of the symplectic group in two…
A basic problem in linear particle optics is to find a symplectic transformation that brings the (symmetric) beam matrix to a special diagonal form, called normal form. The conventional way to do this involves an eigenvalue-decomposition of…
In this paper, we continue to construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation. This procedure now is carried out by constructing solutions to the…
Symplectic integrators are the preferred method of solving conservative $N$-body problems in cosmological, stellar cluster, and planetary system simulations because of their superior error properties and ability to compute orbital…
In this note, we prove that below the first critical energy level, a proper combination of the Ligon-Schaaf and Levi-Civita regularization mappings provides a convex symplectic embedding of the energy surfaces of the planar rotating Kepler…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
The Euler equations associated with diffeomorphism groups have received much recent study because of their links with fluid dynamics, computer vision, and mechanics. In this paper, we consider the dynamics of $N$ point particles or `blobs'…
We study the symplectic reparametrizations that are possible for theories of N=2 supersymmetric vector multiplets in the presence of a chiral background and discuss some of their consequences. One of them concerns an anomaly arising from a…
Euler's three-body problem is the problem of solving for the motion of a particle moving in a Newtonian potential generated by two point sources fixed in space. This system is integrable in the Liouville sense. We consider the Euler problem…
Coherent or exact equations of motion for a post-Newtonian Lagrangian formalism are the Euler-Lagrange equations without any terms truncated. They naturally conserve energy {and} angular momentum. Doubling the phase-space variables of…
We propose a geometric setup to study analytic aspects of a variant of the super symmetric two-dimensional nonlinear sigma model. This functional extends the functional of Dirac-harmonic maps by gravitino fields. The system of…
Modern N-body techniques for planetary dynamics are generally based on symplectic algorithms specially adapted to the Kepler problem. These methods have proven very useful in studying planet formation, but typically require the timestep for…
We apply the dimensional regularization procedure to treat an ultraviolet divergence occurring in the framework of the nuclear many-body problem. We consider the second--order correction (beyond the mean-field approximation) to the equation…
In this paper we regularize the Kepler problem on $\kappa$-spacetime in several different ways. First, we perform a Moser-type regularization and then we proceed for the Ligon-Schaaf regularization to our problem. In particular,…
This paper is concerned with an optimization problem that is constrained by the Kantorovich optimal transportation problem. This bilevel optimization problem can be reformulated as a mathematical problem with complementarity constraints in…
We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…
In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplacian.
We establish a new symmetrization procedure for the isoperimetric problem in symmetric spaces of noncompact type. This symmetrization generalizes the well known Steiner symmetrization in euclidean space. In contrast to the classical…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
It is the goal of this paper to present the first steps for defining the analogue of Hamiltonian Floer theory for covariant field theory, treating time and space relativistically. While there already exist a number of competing geometric…