Vortrag faellt aus wg. Erkrankung! (Non-deterministic billiards)
Manuel Quaschner
Abstract:
In [Kn18], a simple non-deterministic model with three particles was introduced in order to approximate the orbits of solutions of a Hamiltonian equation with admissible potential and at most four bodies that do not have an asymptotic velocity. In these non-deterministic models, near-collisions are substituted by collisions without conservation of kinetic energy. In order to approximate the orbits some properties of non-deterministic models with three particles had to be derived such as the exponential growth (in the number of collisions) of the total kinetic energy and of the moment of inertia or a bound on the angular momenta of each particle in terms of the total angular momentum. All these properties fail to hold in general, if one considers non-deterministic models with more than three particles. Our aim is to investigate these models and derive similar results to the results in the case of three particles. Therefor we have to define another number of collisions in which the growth of the above quantities is exponential by considering a reduced ordered systems of particles moving on a line.