Rotations in the space of Split octonions.
Scattering monodromy and the A 1 singularity
We present the notion of scattering monodromy for a two degree of freedom hyperbolic oscillator and apply this idea to determine the Picard-Lefschetz monodromy of the isolated singular point of a quadratic function of two complex variables.
Separation of variables and the geometry of Jacobians.
Several cohomology algebras connected with Poisson structure.
Several examples of nonholonomic mechanical systems
A unified geometric approach to nonholonomic constrained mechanical systems is applied to several concrete problems from the classical mechanics of particles and rigid bodies. In every of these examples the given constraint conditions are analysed, a corresponding constraint submanifold in the phase space is considered, the corresponding constrained mechanical system is modelled on the constraint submanifold, the reduced equations of motion of this system (i.e. equations of motion defined on the...
Singularities of implicit differential systems and maximum principle
The integrability condition for the Lagrangian implicit differential systems of (TP,ω̇), introduced in [7], is applied for the specialized control theory systems. The Pontryagin maximum principle was reformulated in the framework of implicit differential systems and the corresponding necessary and sufficient conditions were proved. The beginning of the classification list of normal forms for Lagrangian implicit differential systems according to the symplectic equivalence is provided and the corresponding...
Singularities of implicit differential systems and their integrability
Singularities of momentum maps of integrable Hamiltonian systems with two degrees of freedom.
Singularities of wave fronts at the boundary between two media
Sobre los sistemas mecánicos con enlaces.
A mathematical model is proposed in order to describe the behaviour of mechanical systems with constraints.
Solutions d'équations d'Hamilton-Jacobi et géométrie symplectique
Solutions of Minimal Period for a Class of Convex Hamiltonian Systems.
Solutions périodiques de systèmes hamiltoniens sur des surfaces d'énergie étoilées
Solving non-holonomic Lagrangian dynamics in terms of almost product structures.
Given a Lagrangian system with non-holonomic constraints we construct an almost product structure on the tangent bundle of the configuration manifold such that the projection of the Euler-Lagrange vector field gives the dynamics of the system. In a degenerate case, we develop a constraint algorithm which determines a final constraint submanifold where a completely consistent dynamics of the initial system exists.
Some aspects of the homogeneous formalism in field theory and gauge invariance
We propose a suitable formulation of the Hamiltonian formalism for Field Theory in terms of Hamiltonian connections and multisymplectic forms where a composite fibered bundle, involving a line bundle, plays the role of an extended configuration bundle. This new approach can be interpreted as a suitable generalization to Field Theory of the homogeneous formalism for Hamiltonian Mechanics. As an example of application, we obtain the expression of a formal energy for a parametrized version of the Hilbert–Einstein...
Some inequalities satisfied by periodical solutions of multi-time Hamilton equations.
Some remarks about the complete integrability in the sense of Arnold-Liouville.
Some results about dissipativity of Kolmogorov operators
Given a Hilbert space with a Borel probability measure , we prove the -dissipativity in of a Kolmogorov operator that is a perturbation, not necessarily of gradient type, of an Ornstein-Uhlenbeck operator.
Some results in Lagrangian mechanics
We associate to a dynamic equation three different connections and then we consider the meaning of the vanishing of their curvatures. Some peculiarities of the case of autonomous dynamic equation polynomial in the velocities are pointed out. Finally, using the so-called Helmholtz conditions, we investigate a particular example.
Spectral analysis of relativistic atoms -- interaction with the quantized radiation field.