Related papers: Partial Reduction and Delaunay/Deprit Variables

This paper develops the theory of discrete Dirac reduction of discrete Lagrange-Dirac systems with an abelian symmetry group acting on the configuration space. We begin with the linear theory and, then, we extend it to the nonlinear setting…

We give accurate and ergodic numerical methods for semilinear, second-order Langevin stochastic partial differential equations (SPDE). As a byproduct, we also give good geometric numerical methods for their infinite-dimensional Hamiltonian…

We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems,…

For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in…

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…

We show how Langevin diffusions can be interpreted in the context of stochastic Hamiltonian systems with structure-preserving noise and dissipation on reductive Lie groups. Reductive Lie groups provide the setting in which the Lie group…

An alternative proof of Eliashberg-Gromov's C^0-rigidity theorem is presented and a new notion of weak Lie brackets for Hamiltonian vector fields is proposed and compared.

We propose a new method to prove the partitioned Runge--Kutta methods with symplectic conditions for determinate and stochastic Hamiltonian systems are symplectic. We utilize Gr\"obner basis technology which is the one of symbolic…

This is the pdf -version of the author's Ph.D. thesis (1995, ULB, Belgium). The notion of symeplectic symmertic space is introduced and studied via Lie theoretical and symplectic geoemetrical methods. The first chapter concerns basic…

We propose a simple method to reduce a general p-form electrodynamics with respect to the standard Gauss constraints. The canonical structure of the reduced theory displays a p-dependent sign which makes the essential difference between…

We consider the Lagrangian formulation with duplicated variables of dissipative mechanical systems. The application of Noether theorem leads to physical observable quantities which are not conserved, like energy and angular momentum, and…

The purpose of this paper is to shed a new light on classical constructions in enumerative geometry from the view point of derived algebraic geometry. We first prove that the cosection localized virtual cycle of a quasi-smooth derived…

We compute the convex hull in $\mathbb{C}^2$ of an arbitrary finite subgroup of ${\mathbb{C}^*}^2$. The combinatorics are dictated by continued fractions in a natural way. This reproves a theorem of Smilansky, with a slightly stronger…

We investigate Snyder space-time and its generalizations, including Yang and Snyder-de-Sitter spaces, which constitute manifestly Lorenz invariant noncommutative geometries. This work initiates a systematic study of gauge theory on such…

Newtonian mechanics has the concept of an absolute inertial rest frame. Special relativity eliminates the absolute rest frame but continues to require the absolute inertial frame. General relativity solves this for gravity by requiring…

The present paper studies the post-Newtonian dynamics of N bodies in general relativity. We derive covariant equations of translational and rotational motion of N extended bodies having arbitrary distribution of mass and velocity of matter…

We present a new approach to describe the dynamics of an isolated, gravitationally bound astronomical $N$-body system in the weak field and slow-motion approximation of the general theory of relativity. Celestial bodies are described using…

We present reduction and reconstruction procedures for the solutions of symmetric stochastic differential equations, similar to those available for ordinary differential equations. Additionally, we use the local tangent-normal…

This article belongs to the area of geometric tomography, which is the study of geometric properties of solids based on data about their sections and projections. We describe a new direction in geometric tomography where different…

There is a well developed and useful theory of Hamiltonian reduction for semidirect products, which applies to examples such as the heavy top, compressible fluids and MHD, which are governed by Lie-Poisson type equations. In this paper we…