Related papers: Mould Calculus for Hamiltonian Vector Fields

In this work we revisit and extend the method introduced by Lins Neto, Sad and Sc\'{a}rdua for detecting the non-existence of invariant algebraic curves other than some prescribed invariant nodal curve. We prove that, under the existence of…

We study, theoretically and experimentally, a 1-parameter family of transformations and their limiting vector field on the space of plane polygons. These transformations are discrete analogs of completely integrable transformation on closed…

Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…

We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a…

We prove a theorem which asserts that the Lie algebra of all holomorphic vector fields on a compact K\"ahler manifold with a perturbed extremal metric has the structure similar to the case of an unperturbed extremal K\"ahler metric proved…

We prove a companion forms theorem for mod l Hilbert modular forms. This work generalises results of Gross and Coleman--Voloch for modular forms over Q, and gives a new proof of their results in many cases. The methods used are completely…

Many well-known theorems establish sufficient criteria for linearizability of a vector field in terms of the eigenvalues of its linear approximation. By attaching weights to coordinates so that some directions are considered "linear",…

We prove the formality theorem for the differential graded Lie algebra module of Hochschild chains for the algebra of endomorphisms of a smooth vector bundle. We discuss a possible application of this result to a version of the algebraic…

In this article, we prove that a free divisor in a three dimensional complex manifold must be Euler homogeneous in a strong sense if the cohomology of its complement is the hypercohomology of its logarithmic differential forms. F.J.…

We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.

In this paper we develop the vectorial Ribaucour transformation for Euclidean submanifolds. We prove a general decomposition theorem showing that under {appropriate} conditions the composition of two or more vectorial Ribaucour…

In this paper, we investigate vector fields on polyhedral complexes and their associated trajectories. We study vector fields which are analogue of the gradient vector field of a function in the smooth case. Our goal is to define a nice…

In this study, we introduce the theory of what we call Hecke vector-forms. A Hecke vector-form can be viewed as a vector function representation of some quasiautomorphic form that transforms like an automorphic form on an arbitrarily chosen…

We study a perturbative scheme for normalization problems involving resonances of the unperturbed situation, and therefore the necessity of a non-trivial normal form, in the general framework of Banach scale Lie algebras (this notion is…

In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…

We show the existence of formal equivalences between reversible and Hamiltonian vector fields. The main tool we employ is the normal form theory.

This work deals with several aspects of the extension to Abelian Higgs models of the deformation method originally developed for scalar field models. We present several examples allowing to transform self-dual solutions of different…

Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a sphere. The fields basically…

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. While the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory…

A natural explicit condition is given ensuring that an action of the multiplicative monoid of non-negative reals on a manifold F comes from homotheties of a vector bundle structure on F, or, equivalently, from an Euler vector field. This is…