Separability of the characteristic polynomial
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...
Singularités, sources de quelques métriques stationnaires
Singularities of momentum maps of integrable Hamiltonian systems with two degrees of freedom.
Some concepts of regularity for parametric multiple-integral problems in the calculus of variations
We show that asserting the regularity (in the sense of Rund) of a first-order parametric multiple-integral variational problem is equivalent to asserting that the differential of the projection of its Hilbert-Carathéodory form is multisymplectic, and is also equivalent to asserting that Dedecker extremals of the latter -form are holonomic.
Sui moti polinomiali
Sul teorema di Liouville per deformazioni conformi
Sur la description intrinsèque des grandeurs dimensionnelles
Sur la dynamique des systèmes mécaniques
Symmetries and currents in nonholonomic mechanics
In this paper we derive general equations for constraint Noethertype symmetries of a first order non-holonomic mechanical system and the corresponding currents, i.e. functions constant along trajectories of the nonholonomic system. The approach is based on a consistent and effective geometrical theory of nonholonomic constrained systems on fibred manifolds and their jet prolongations, first presented and developed by Olga Rossi. As a representative example of application of the geometrical theory...
Symmetries of second-order potential differential systems.
Symplectic topology of integrable hamiltonian systems, I : Arnold-Liouville with singularities
Systèmes hamiltoniens k-symplectiques.
We study some properties of the k-symplectic Hamiltonian systems in analogy with the well-known classical Hamiltonian systems. The integrability of k-symplectic Hamiltonian systems and the relationships with the Nambu's statistical mechanics are given.
Taylor obstruction to the integrability of homogeneous potentials of degree two. An application of higher order variational equations
We show how using the differential Galois theory one can find effectively necessary conditions for the integrability of Hamiltonian systems with homogeneous potentials.
Tensor fields defining a tangent bundle structure
Teorie dynamických systémů
The averaging of nonlocal Hamiltonian structures in Whitham's method.
The complex geometry of an integrable system
In this paper, a finite dimensional algebraic completely integrable system is considered. We show that the intersection of levels of integrals completes into an abelian surface (a two dimensional complex algebraic torus) of polarization and that the flow of the system can be linearized on it.
The finitary isomorphism problem for one-dimensional Gibbs systems of molecular type
The geometry and mechanics of multi-particle systems