Related papers: Euler-Poincare reduction for discrete field theori…

Motivated by decompositions of spaces that arise in continuous and discrete Morse theory, we describe a so called fibrous decomposition Z = X_0(Y_1)X_1 ... X_{n-1}(Y_n)X_n of a space Z. Among the applications is a succinct formula for the…

Based on the simple and well understood concept of subfields in a finite field, the technique called `field reduction' has proved to be a very useful and powerful tool in finite geometry. In this paper we elaborate on this technique. Field…

We discuss the local behaviour of vector fields in the plane $\R^2$ around a regular singular point, using recently introduced reduced normal forms, i.e. Poincar\'e and Lie renormalized forms [{\it Lett. Math. Phys.} {\bf 42} (1997),…

We investigate a non-trivial extension of the $D-$dimensional Poincar\'e algebra. Matrix representations are obtained. The bosonic multiplets contain antisymmetric tensor fields. It turns out that this symmetry acts in a natural geometric…

We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these…

Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…

The Euler-Poincare characteristic, or Euler characteristic in short, is a fundamental topological invariant of compact manifolds that plays a crucial role in a variety of geometric and topological situations. From this point of view, we…

The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of…

In the frame of the Lagrangian formalism on $r$-order prolongations of fibered manifolds and related structures such as (prolongation of) projectable vector fields, (sheaves of) differential forms and contact structures, we propose a…

We construct some intrinsically defined discrete model of the magnetic Laplacian. The existence and uniqueness of solutions of the Dirichlet problem for the difference Poisson type equation are proved. We study in detail properties of the…

In a space of 4-dimensions, I will examine constrained variational problems in which the Lagrangian, and constraint scalar density, are concomitants of a (pseudo-Riemannian) metric tensor and its first two derivatives. The Lagrange…

We discuss the notion of reduction of a special type of explicit solutions which generalize the solutions appearing in the classical Laplace cascade method of integration of hyperbolic equations of the second order in the plane. We give…

In this work we introduce a category $LDP_d$ of discrete-time dynamical systems, that we call discrete Lagrange--D'Alembert--Poincar\'e systems, and study some of its elementary properties. Examples of objects of $LDP_d$ are nonholonomic…

We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of application are studied, in particular,…

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange-Dirac and…

Finite Euler hierarchies of field theory Lagrangians leading to universal equations of motion for new types of string and membrane theories and for {\it classical} topological field theories are constructed. The analysis uses two main…

Employing a phase space which includes the (Riemann-Liouville) fractional derivative of curves evolving on real space, we develop a restricted variational principle for Lagrangian systems yielding the so-called restricted fractional…

This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the covariant Euler-Poincar\'e equations that naturally includes…

A new construction of Euler-Poincar\'e functions for real reductive groups is given. This construction also works for non-connected groups and representations that do not lift.

This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…