Classical Planar Scattering by Coulombic Potentials

Shows the chaotic behaviour of classical scattering at Coulomb singularities. This result is presented in depth, aiming to appeal to a wide readership in mathematics and physics.

---

This book treats scattering of a classical particle in a scalar potential with one or more attracting Coulombic singularities. For more than two centers this is an important prototype of chaotic scattering, which is analysed in depth here using methods of differential geometry and ergodic theory. In particular, the Cantor-set structure of all bounded orbits is described in terms of symbolic dynamics, and rigorous energy-dependent bounds are derived for quantities such as the topological entropy of the flow, the Hausdorff dimension of the bounded orbits, and the distribution of time delay. This shows that the chaotic behaviour of such systems is universal in the high-energy regime. Finally the scattering orbits are classified by use of a group. A mathematically rigorous and comprehensive treatment of chaotic scattering in Coulombic potentials, including 13 figures, is given The book of interest to mathematical physicists, mathematicians, and physicists.