A gentle (without chopping) approach to the full Kostant-Toda lattice.
A journey between two curves.
A recursive scheme of first integrals of the geodesic flow of a Finsler manifold.
A super-integrable two-dimensional nonlinear oscillator with an exactly solvable quantum analog.
A system of coupled oscillators with magnetic terms: symmetries and integrals of motion.
Algebraic calculation of the energy eigenvalues for the nondegenerate three-dimensional Kepler-Coulomb potential.
Algebro-geometric Integration in Classical and Statistical Mechanics
Bäcklund transformation for the BC-type Toda lattice.
Bäcklund transformations for the Kirchhoff top.
Bäcklund transformations for the trigonometric Gaudin magnet.
Classical particle in presence of magnetic field, hyperbolic Lobachevsky and spherical Riemann models.
Completely integrable systems associated with classical root systems.
Cruising in a central force field.
Geometric study of a family of integrable systems. (Étude géométrique d'une famille de systémes intégrables.)
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.
Integrable Hamiltonian systems on Lie groups: Kowalewski type.
Integrable systems, Poisson pencils, and hyperelliptic Lax pairs
Isospectrality for quantum toric integrable systems
We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians. This type of...
Levi-flat invariant sets of holomorphic symplectic mappings
We classify four families of Levi-flat sets which are defined by quadratic polynomials and invariant under certain linear holomorphic symplectic maps. The normalization of Levi- flat real analytic sets is studied through the technique of Segre varieties. The main purpose of this paper is to apply the Levi-flat sets to the study of convergence of Birkhoff's normalization for holomorphic symplectic maps. We also establish some relationships between Levi-flat invariant sets...
Models for quadratic algebras associated with second order superintegrable systems in 2D.