A geometric setting for classical molecular dynamics
An energy conserving modification of numerical methods for the integration of equations of motion.
Collision and stable regions around bodies with simple geometric shape.
Convergenza per l'equazione degli integrali primi associata al problema del rimbalzo
In this paper we present a few results on convergence for the prime integrals equations connected with the bounce problem. This approach allows both to prove uniqueness for the one-dimensional bounce problem for almost all permissible Cauchy data (see also [6]) and to deepen previous results (see [3], [5], [7]).
Dynamical systems with Newtonian type potentials
We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.
Errata : “Generators for quasi-free completely positive semi-groups”
Extension des relations de Frenet aux courbes à points irréguliers
Generators for quasi-free completely positive semi-groups
Geometrical Aspects of the Circular Billiard Problem.
Gli universi ipersferici, il gruppo conforme ed il campo gravitazionale di Newton.
Introduction to algorithms for molecular simulations
In the first part of the paper we survey some algorithms which describe time evolution of interacting particles in a bounded domain. Applications to macroscale as well as microscale are presented on two examples: motion of planets and collision of two bodies. In the second part of the paper we present solution to stationary Schrödinger equation for simple molecular models.
Kepler-Newton-Coulomb system and Lie matrix spin (incomplete).
Measure-differential inclusions in percussional dynamics.
Motion of a particle submitted to dry friction and to normal percussions.
On central configurations.
On integration of the differential equation of central motion, I
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
On the derivation of a quantum Boltzmann equation from the periodic Von-Neumann equation
We present the semi-conductor Boltzmann equation, which is time-reversible, and indicate that it can be formally derived by considering the large time and small perturbing potential limit in the Von-Neumann equation (time-reversible). We then rigorously compute the corresponding asymptotics in the case of the Von-Neumann equation on the Torus. We show that the limiting equation we obtain does not coincide with the physically realistic model. The former is indeed an equation of Boltzmann type, yet...
Periodic derivative of solutions to nonlinear differential equations
Precession of the perihelion within a generalized theory for the two body problem
Sulla base di una teoria generalizzata di Meccanica Classica per il problema dei Due Corpi, recentemente formulata dall'autore, si considera la questione della precessione del perielio dei pianeti, assente nel caso Newtoniano. Si mostra come la descrizione di questo fenomeno in tale teoria generalizzata è sostanzialmente equivalente a quella offerta dalla Relatività Generale.