A convexity theorem for Poisson actions of compact Lie groups
A system of coupled oscillators with magnetic terms: symmetries and integrals of motion.
Abstract mechanical connection and Abelian reconstruction for almost Kähler manifolds.
Almost product structures and Poisson reduction of presymplectic systems.
An alternative canonical approach to the ghost problem in a complexified extension of the Pais-Uhlenbeck oscillator.
Classification of symmetries for higher order Lagrangian systems II: The non-autonomous case.
Classification of symmetries for higher order Lagrangian systems.
Complexification of proper hamiltonian -spaces
Convexity Properties of the Moment Mapping.
Discrete Euler-Poincaré and Euler Poincaré-Poisson equations for semidirect products and principal bundles.
Dynamical systems and Lagrangian spaces.
Equivariant normal form for nondegenerate singular orbits of integrable hamiltonian systems
Ergodic averages and free actions
If the ergodic transformations S, T generate a free action on a finite non-atomic measure space (X,S,µ) then for any there exists a measurable function f on X for which and -almost everywhere as N → ∞. In the special case when S, T are rationally independent rotations of the circle this result answers a question of M. Laczkovich.
Generalized PN manifolds and separation of variables
The notion of generalized PN manifold is a framework which allows one to get properties of first integrals of the associated bihamiltonian system: conditions of existence of a bi-abelian subalgebra obtained from the momentum map and characterization of such an algebra linked with the problem of separation of variables.
Geometric Quantization and Multiplicities of Group Representations.
Geometric quantization and no-go theorems
A geometric quantization of a Kähler manifold, viewed as a symplectic manifold, depends on the complex structure compatible with the symplectic form. The quantizations form a vector bundle over the space of such complex structures. Having a canonical quantization would amount to finding a natural (projectively) flat connection on this vector bundle. We prove that for a broad class of manifolds, including symplectic homogeneous spaces (e.g., the sphere), such connection does not exist. This is a...
Geometrical aspects of the Landau-Hall problem on the hiperbolic plane.
Se discuten algunos aspectos del problema de Landau-Hall hiperbólico. El álgebra de Lie de las simetrías infinitesimales de este problema se da explícitamente, resultando ser isomorfa a so(2,1) y que sus invariantes Noether asociados son los momentos angulares hiperbólicos. Asimismo se desarrolla la formulación hamiltoniana, lo que nos permitirá obtener la variedad de órbitas de energía constante de este problema mediante técnicas de reducción simpléctica.
Hierarchy of integrable geodesic flows.
A family of integrable geodesic flows is obtained. Any such a family corresponds to a pair of geodesically equivalent metrics.
Infinitely many homoclinic orbits for Hamiltonian systems with group symmetries.
Invariante Variationsprobleme