A double chain of coupled circuits in analogy with mechanical lattices.
A new Lagrangian dynamic reduction in field theory
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
A survey on Nambu-Poisson brackets.
Algèbres de Lie, systèmes hamiltoniens, courbes algébriques
Canonical formulation of newtonian dynamics
Comment by the editors on the paper : “The hamiltonian formalism in higher order variational problems”
Critical diffusions
Critical Point Theorems for Indefinite Functionals.
Dirac brackets in geometric dynamics
Erratum : “On the geometry of subbundles and Lagrange foliations”
Erratum : “The quantum stability problem for time-periodic perturbations of the harmonic oscillator”
Fundamental vector fields on type fibres of jet prolongations of tensor bundles
Nambu-Lie group actions.
New trends in mechanics. I. Generalized differential variational principles in rational mechanics.
Normal Modes for Nonlinear Hamiltonian Systems.
On a horizontal structure on differentiable manifolds
On a Trace Functional for Formal Pseudo-Differential Operators and the Symplectic Structure of the Korteweg-Devries Type Equation.
On decomposability of Nambu-Poisson tensor.
On the algebraic structure on the jet prolongations of fibred manifolds
Poincaré-Cartan forms in higher order variational calculus on fibred manifolds.
The aim of the present work is to present a geometric formulation of higher order variational problems on arbitrary fibred manifolds. The problems of Engineering and Mathematical Physics whose natural formulation requires the use of second order differential invariants are classic, but it has been the recent advances in the theory of integrable non-linear partial differential equations and the consideration in Geometry of invariants of increasingly higher orders that has highlighted the interest...