On Elliptic Lower Dimensional Tori in Hamiltonian Systems.
On embedding the 1:1:2 resonance space in a Poisson manifold.
On Fixed Points of Symplectic Maps.
On minimal sets in 2-manifolds.
On quadratic symplectic mappings.
On the application of control theory to certain problems for Lagrangian systems, and hyper-impulsive motion for these. I. Some general mathematical considerations on controllizable parameters
In applying control (or feedback) theory to (mechanic) Lagrangian systems, so far forces have been generally used as values of the control . However these values are those of a Lagrangian co-ordinate in various interesting problems with a scalar control , where this control is carried out physically by adding some frictionless constraints. This pushed the author to consider a typical Lagrangian system , referred to a system of Lagrangian co-ordinates, and to try and write some handy conditions,...
On the density of the range for some nonlinear operators
On the existence and non-existence of closed trajectories for some Hamiltonian flows.
On the existence of homoclinic solutions for almost periodic second order systems
On the geometric structure of the set of solutions of Einstein equations [Book]
On the -instability and -controllability of steady flows of an ideal incompressible fluid
In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady flow is unstable...
On the Lagrange-Souriau form in classical field theory
The Euler-Lagrange equations are given in a geometrized framework using a differential form related to the Poincare-Cartan form. This new differential form is intrinsically characterized; the present approach does not suppose a distinction between the field and the space-time variables (i.e. a fibration). In connection with this problem we give another proof describing the most general Lagrangian leading to identically vanishing Euler-Lagrange equations. This gives the possibility to have a geometric...
On the mechanics with noncontinuous hamiltonians
On the optimal control of implicit systems
On the optimal control of implicit systems
In this paper we consider the well-known implicit Lagrange problem: find a trajectory solution of an underdetermined implicit differential equation, satisfying some boundary conditions and which is a minimum of the integral of a Lagrangian. In the tangent bundle of the surrounding manifold X, we define the geometric framework of q-pi- submanifold. This is an extension of the geometric framework of pi- submanifold, defined by Rabier and Rheinboldt for determined implicit differential equations,...
On the prescribed-period problem for autonomous Hamiltonian systems.
On the question of stability in a Hamiltonian system
On the Symplectic Structure of Coadjoint Orbits of (Solvable) Lie Groups and Applications. I.
On the topological charge conservation in the three-dimensional -model.
A field of three-component unit vectors on the dimensional spacetime is considered. Two field configurations with different values of the topological charge cannot be connected by the path of field configurations with a finite Euclidean action. Therefore there is no transition between them. The initial and final configurations are assumed to be continuous at infinity. The asymptotic behaviour of intermediate configurations may be arbitrary. The proof is based on the properties of the degree of...
On the transversal distribution and the complete figure in the second order multiple integral problem in the calculus of variations.