Related papers: Partial Reduction and Delaunay/Deprit Variables
The Marsden-Weinstein-Meyer symplectic reduction has an analogous version for cosymplectic manifolds. In this paper we extend this cosymplectic reduction to the context of groupoids. Moreover, we prove how in the case of an algebroid…
The $N$-body problem is of historical significance because it was the first implementation of the Newtonian dynamical laws for the description of our Solar System. Motivated by this, the project's goal is to revisit this problem for small…
The inverse problem of the calculus of variations consists in determining if the solutions of a given system of second order differential equations correspond with the solutions of the Euler-Lagrange equations for some regular Lagrangian.…
In this note we give conditions which ensure the reduction of a symplectic connection in the process of a Marsden-Weinstein reduction and of the reduction of a presymplectic manifold.
This article concerns cotangent-lifted Lie group actions; our goal is to find local and ``semi-global'' normal forms for these and associated structures. Our main result is a constructive cotangent bundle slice theorem that extends the…
A Lie system is a non-autonomous system of first-order ordinary differential equations describing the integral curves of a non-autonomous vector field taking values in a finite-dimensional real Lie algebra of vector fields, a so-called…
We present a numerical weak-lensing analysis that is fully relativistic and non-perturbative for the scalar part of the gravitational potential and first-order in the vector part, frame dragging. Integrating the photon geodesics backwards…
We prove that the derived critical locus of a $G$-invariant function $S:X\to\mathbb{A}^1$ carries a shifted moment map, and that its derived symplectic reduction is the derived critical locus of the induced function…
A two-dimensional integrable system being a deformation of the rational Calogero-Moser system is constructed via the symplectic reduction, performed with respect to the Sklyanin algebra action. We explicitly resolve the respective classical…
In this paper, we consider the elliptic relative equilibria of four-body problem. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic relative equilibria of $4$-bodies splits into two independent linear…
The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by…
We study the partial breaking of $N=2$ rigid supersymmetry for a generic rigid special geometry of $n$ abelian vector multiplets in the presence of Fayet-Iliopoulos terms induced by the Hyper-K\"ahler momentum map. By exhibiting the…
In this work we propose a new numerical approach to distinguish between regular and chaotic orbits in Hamiltonian systems, based on the simultaneous integration of both the orbit and the deviation vectors using a symplectic scheme, hereby…
This survey has multiple objectives. First, we motivate and review a new distributional notion of the d'Alembertian from mathematical relativity, more precisely, a nonlinear $p$-version thereof, where $p$ is a nonzero number less than one.…
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…
We present general reduction procedures for Courant, Dirac and generalized complex structures, in particular when a group of symmetries is acting. We do so by taking the graded symplectic viewpoint on Courant algebroids and carrying out…
Hill's equations are an approximation that is useful in a number of areas of astrophysics including planetary rings and planetesimal disks. We derive a symplectic method for integrating Hill's equations based on a generalized leapfrog. This…
This work is devoted to study the relation between regularity and decay of solutions of some dissipative perturbations of the Korteweg-de Vries equation in weighted and asymmetrically weighted Sobolev spaces.
We derive the complete and optimal Cheng--Yau gradient estimates and universal bounds for subcritical semilinear elliptic equations on Riemannian manifolds with (Bakry-\'{E}mery) Ricci curvature bounded below. This answers a fundamental…
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.