Approximation of mixing point configuration spaces over by spaces of set configurations
Blow up of mechanical systems with a homogeneous energy.
By using the ideas introduced by McGehee in the study of the singularities in some problems of Celestial Mechanics, we study the singularities at the origin and at the infinity for some classical mechanical systems with homogeneous kinetic and potential energy functions. For these systems the origin and the infinity of the configuration coordinates is usually a singularity or a nullity of the Hamiltonian function and the verctor field. This work generalizes a previous one by the first and the third...
Corrections to "L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper triangular matrices" (Fund. Math. 156 (1998), 99–110)
Embedding set configuration spaces into those of Ruelle's point configurations
Equilibrium configurations and small oscillations of some dynamical systems
Generalized Lagrange-d'Alembert Principle
Geometric quantization of the MIC-Kepler problem via extension of the phase space
Infinitesimal symplectic relations and generalized hamiltonian dynamics
Internal properness and stability in linear systems
L2 -characteristic classes of Maslov–Trofimov of hamiltonian systems on the Lie algebra of the upper-triangular matrices
We generalize the construction of Maslov-Trofimov characteristic classes to the case of some G-manifolds and use it to study certain hamiltonian systems.
Nonautonomous dynamical systems and associated fields. (Systèmes dynamiques nonautonomous et des champs associés.)
Non-decomposable Nambu brackets
It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e. given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darboux-like Theorem via a Nambu-type generalization of Weinstein’s splitting principle for Poisson manifolds.
Non-holonomic mechanical systems in jet bundles.
In this paper we present a geometrical formulation for Lagrangian systems subjected to non-holonomic constraints in terms of jet bundles. Cosymplectic geometry and almost product structures are used to obtained the constrained dynamics without using Lagrange multipliers method.
On the existence of equations of evolution.
On the question of stability in a Hamiltonian system
Pursuit in physical spaces
Quantization and global properties of manifolds
Quantization on submanifolds
Separability of the characteristic polynomial
Sul teorema di Liouville per deformazioni conformi