The fifth International School ~ Mathematical Physics was held at
the Ettore Majorana Centro della Culture Scientifica, Erice,
Sicily, 2 to 14 July 1983. The present volume collects lecture
notes on the session which was devoted to'Regular and Chaotic
Motions in Dynamlcal Systems. The School was a NATO Advanced Study
Institute sponsored by the Italian Ministry of Public Education,
the Italian Ministry of Scientific and Technological Research and
the Regional Sicilian Government. Many of the fundamental problems
of this subject go back to Poincare and have been recognized in
recent years as being of basic importance in a variety of physical
contexts: stability of orbits in accelerators, and in plasma and
galactic dynamics, occurrence of chaotic motions in the excitations
of solids, etc. This period of intense interest on the part of
physicists followed nearly a half a century of neglect in which
research in the subject was almost entirely carried out by
mathematicians. It is an in dication of the difficulty of some of
the problems involved that even after a century we do not have
anything like a satisfactory solution.
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