4 Recherche d'orbites périodiques d'un champ hamiltonien associé à une structure symplectique non standard
A BF-regularization of a nonstationary two-body problem under the Maneff perturbing potential.
The process of transforming singular differential equations into regular ones is known as regularization. We are specially concerned with the treatment of certain systems of differential equations arising in Analytical Dynamics, in such a way that, accordingly, the regularized equations of motion will be free of singularities.
A characterization of tangent and stable tangent bundles
A class of Hamiltonian systems with increasing periods.
A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems.
A completion of A. Bressan's work on axiomatic foundations of the Mach Painlevé type for various classical theories of continuous media. Part 1. Completion of Bressan's work based on the notion of gravitational equivalence of affine inertial frames
The work [3], where various classical theories on continuous bodies are axiomatized from the Mach-Painlevè point of view, is completed here in two alternative ways; in that work, among other things, affine inertial frames are defined within classical kinematics. Here, in Part I, a thermodynamic theory of continuous bodies, in which electrostatic phenomena are not excluded, is dealt with. The notion of gravitational equivalence among affine inertial frames and the notion of gravitational isotropy...
A deterministic displacement theorem for Poisson processes.
A discretization of the nonholonomic Chaplygin sphere problem.
A double chain of coupled circuits in analogy with mechanical lattices.
A first-order canonical set of generalized Jacobi-type variables for hyperbolic orbital motion.
A gentle (without chopping) approach to the full Kostant-Toda lattice.
A geometric analysis of dynamical systems with singular Lagrangians
We study dynamics of singular Lagrangian systems described by implicit differential equations from a geometric point of view using the exterior differential systems approach. We analyze a concrete Lagrangian previously studied by other authors by methods of Dirac’s constraint theory, and find its complete dynamics.
A geometric mechanism for diffusion in Hamiltonian systems overcoming the large gap problem: announcement of results.
A Hamiltonian approach to the discrete-continuous dynamical systems in diamond-type crystals.
A journey between two curves.
A methodology for the numerical computation of normal forms, centre manifolds and first integrals of Hamiltonian systems.
A new geometric setting for classical field theories
A new geometrical setting for classical field theories is introduced. This description is strongly inspired by the one due to Skinner and Rusk for singular lagrangian systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.
A new geometrical framework for time-dependent Hamiltonian mechanics.
A new Lagrangian dynamic reduction in field theory
For symmetric classical field theories on principal bundles there are two methods of symmetry reduction: covariant and dynamic. Assume that the classical field theory is given by a symmetric covariant Lagrangian density defined on the first jet bundle of a principal bundle. It is shown that covariant and dynamic reduction lead to equivalent equations of motion. This is achieved by constructing a new Lagrangian defined on an infinite dimensional space which turns out to be gauge group invariant.
A new look at classical mechanics of constrained systems