ENGLISH

Classical planar scattering by Coulombic potentials

By Andreas Knauf , Markus Klein

Book information

Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Year
1992
ISBN
9783540559870, 3540559876
Language
english
Format
PDF
Filesize
6 MB (6745681 bytes)
Series
Lecture Notes in Physics
Pages
138\138
Topic
Physics
Time added
2009-08-06 05:14:26

Description

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. Most of the results in the book are new. The first mathematically rigorous and comprehensive treatment of chaotic scattering in Coulombic potentials, including 13 figures are given. The book will be of interest to mathematical physicists, mathematicians, and physicists.

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