Multibump solutions for a class of lagrangian systems slowly oscillating at infinity
Multiple closed orbits for singular conservative systems via geodesic theory
Multiple homoclinic orbits for a class of conservative systems
Multiple orbits for hamiltonian systems on starshaped surfaces with symmetries
Multiple solutions for a class of -Laplacian systems.
Multiplicity of Subharmonic solutions of Forces Hamiltonian systems near an equilibrium.
Nekhoroshev estimates for quasi-convex hamiltonian systems.
Non singular Hamiltonian systems and geodesic flows on surfaces with negative curvature.
We extend here results for escapes in any given direction of the configuration space of a mechanical system with a non singular bounded at infinity homogeneus potential of degree -1, when the energy is positive. We use geometrical methods for analyzing the parallel and asymptotic escapes of this type of systems. By using Riemannian geometry methods we prove under suitable conditions on the potential that all the orbits escaping in a given direction are asymptotically parallel among themselves. We...
Nontrivial periodic solutions for strong resonance hamiltonian systems
On a deformed version of the two-disk dynamo system
We give some deformations of the Rikitake two-disk dynamo system. Particularly, we consider an integrable deformation of an integrable version of the Rikitake system. The deformed system is a three-dimensional Hamilton-Poisson system. We present two Lie-Poisson structures and also symplectic realizations. Furthermore, we give a prequantization result of one of the Poisson manifold. We study the stability of the equilibrium states and we prove the existence of periodic orbits. We analyze some properties...
On Carnot's theorem in time dependent impulsive mechanics.
We show that the validity of the Carnot's theorem about the kinetic energy balance for a mechanical system subject to an inert impulsive kinetic constraint, once correctly framed in the time dependent geometric environment for Impulsive Mechanics given by the left and right jet bundles of the space-time bundle N, is strictly related to the frame of reference used to describe the system and then it is not an intrinsic property of the mechanical system itself. We analyze in details the class of frames...
On classical intrinsically resonant formal perturbation theory
On Liouville forms
We give different notions of Liouville forms, generalized Liouville forms and vertical Liouville forms with respect to a locally trivial fibration π:E → M. These notions are linked with those of semi-basic forms and vertical forms. We study the infinitesimal automorphisms of these forms; we also investigate the relations with momentum maps.
On one approach to investigation of mechanical systems.
On singularities of Hamiltonian mappings
The notion of an implicit Hamiltonian system-an isotropic mapping H: M → (TM,ω̇) into the tangent bundle endowed with the symplectic structure defined by canonical morphism between tangent and cotangent bundles of M-is studied. The corank one singularities of such systems are classified. Their transversality conditions in the 1-jet space of isotropic mappings are described and the corresponding symplectically invariant algebras of Hamiltonian generating functions are calculated.
On submanifolds and quotients of Poisson and Jacobi manifolds
We obtain conditions under which a submanifold of a Poisson manifold has an induced Poisson structure, which encompass both the Poisson submanifolds of A. Weinstein [21] and the Poisson structures on the phase space of a mechanical system with kinematic constraints of Van der Schaft and Maschke [20]. Generalizations of these results for submanifolds of a Jacobi manifold are briefly sketched.
On the existence and non-existence of closed trajectories for some Hamiltonian flows.
On the Isoenergetical Non-Degeneracy of the Problem of two Centers of Gravitation
* Partialy supported by contract MM 523/95 with Ministry of Science and Technologies of Republic of Bulgaria.For the system describing the motion of a moss point under the action of two static gravity centers (with equal masses), we find a subset of the set of the regular values of the energy and momentum, where the condition of isoenergetical non-degeneracy is fulfilled.
On the mechanics with noncontinuous hamiltonians
On the multiplicity of brake orbits and homoclinics in Riemannian manifolds
Let be a complete Riemannian manifold, an open subset whose closure is diffeomorphic to an annulus. If is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in starting orthogonally to one connected component of and arriving orthogonally onto the other one. The results given in [5] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating...