The equivalence between the Hamiltonian and Lagrangian formulations for the parametrization-invariant theories.
The equivalence of controlled lagrangian and controlled hamiltonian systems
The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The Equivalence of Controlled Lagrangian and Controlled Hamiltonian Systems
The purpose of this paper is to show that the method of controlled Lagrangians and its Hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying Lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The first Birkhoff coefficient and the stability of 2-periodic orbits on billiards.
The -graded symplectic Floer cohomology of monotone Lagrangian submanifolds.
The hamiltonian formalism in higher order variational problems
The Helmholtz conditions for the difference equations systems.
The -centre problem of celestial mechanics for large energies
We consider the classical three-dimensional motion in a potential which is the sum of attracting or repelling Coulombic potentials. Assuming a non-collinear configuration of the centres, we find a universal behaviour for all energies above a positive threshold. Whereas for there are no bounded orbits, and for there is just one closed orbit, for the bounded orbits form a Cantor set. We analyze the symbolic dynamics and estimate Hausdorff dimension and topological entropy of this hyperbolic set....
The shadowing chain lemma for singular Hamiltonian systems involving strong forces
We consider a planar autonomous Hamiltonian system :q+∇V(q) = 0, where the potential V: ℝ2 {ζ→ ℝ has a single well of infinite depth at some point ζ and a strict global maximum 0at two distinct points a and b. Under a strong force condition around the singularity ζ we will prove a lemma on the existence and multiplicity of heteroclinic and homoclinic orbits - the shadowing chain lemma - via minimization of action integrals and using simple geometrical arguments.
The symplectic structure of curves in three dimensional spaces of constant curvature and the equations of mathematical physics
Totally singular Lagrangians and affine Hamiltonians.
Trajectoires bornées d'une particule soumise à un champ magnétique symétrique linéaire
Transition le long des chaînes de tores invariants pour les systèmes hamiltoniens analytiques