Scalar-flat Kähler metrics with SU (2) symmetry.
Scattered homoclinics to a class of time-recurrent Hamiltonian systems
A second-order Hamiltonian system with time recurrence is studied. The recurrence condition is weaker than almost periodicity. The existence is proven of an infinite family of solutions homoclinic to zero whose support is spread out over the real line.
Second order superintegrable systems in three dimensions.
Semiclassical limit for perturbations of non-resonant rotators
Separation of variables and the geometry of Jacobians.
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...
Singular Bohr–Sommerfeld rules for 2D integrable systems
Singular fibres of the momentum mapping for integrable Hamiltonian systems.
Singular Hamiltonian systems and symplectic capacities
The purpose of this paper is to develop the basics of a theory of Hamiltonian systems with non-differentiable Hamilton functions which have become important in symplectic topology. A characteristic differential inclusion is introduced and its equivalence to Hamiltonian inclusions for certain convex Hamiltonians is established. We give two counterexamples showing that basic properties of smooth systems are violated for non-smooth quasiconvex submersions, e.g. even the energy conservation which nevertheless...
Singular separatrix splitting and the Melnikov method: An experimental study.
Singularities in contact geometry
In the first half of the paper, we consider singularities of infinitesimal contact transformations and first order partial differential equations, the main results being related to the classical Sternberg-Chen theorem for hyperbolic germs of vector fields. The second half explains how to construct global generating phase functions for solutions of Hamilton-Jacobi equations and see what their singularities look like.
Singularities of implicit differential systems and their integrability
Singularities of momentum maps of integrable Hamiltonian systems with two degrees of freedom.
Slow and fast systems with Hamiltonian reduced problems.
Small divisors and large multipliers
We study germs of singular holomorphic vector fields at the origin of of which the linear part is -resonant and which have a polynomial normal form. The formal normalizing diffeomorphism is usually divergent at the origin but there exists holomorphic diffeomorphisms in some “sectorial domains” which transform these vector fields into their normal form. In this article, we study the interplay between the small divisors phenomenon and the Gevrey character of the sectorial normalizing diffeomorphisms....
Smooth Gevrey normal forms of vector fields near a fixed point
We study germs of smooth vector fields in a neighborhood of a fixed point having an hyperbolic linear part at this point. It is well known that the “small divisors” are invisible either for the smooth linearization or normal form problem. We prove that this is completely different in the smooth Gevrey category. We prove that a germ of smooth -Gevrey vector field with an hyperbolic linear part admits a smooth -Gevrey transformation to a smooth -Gevrey normal form. The Gevrey order depends on...
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 DEs and PDEs as potential maps using first order Lagrangians.
Solutions périodiques de systèmes hamiltoniens