Abstract
Recent developments in the theory of non-linear Hamiltonian dynamics have changed the way in which classical phase space should be viewed. This change in viewpoint has been absorbed by workers in semi-classical quantization of the energy levels of systems of several coupled degrees of freedom, but is only recently having an impact on our thinking about atomic and molecular dynamics. What is done in these lectures is to introduce the elementary concepts needed to understand the nature and structure of chaotic phase space, and the role of time independent phase space structures on the dynamical processes controlled by them. Many illustrations involving the dynamics of classical two degree of freedom systems are introduced, and hints at generalization to higher numbers of active degrees of freedom, and to the inclusion of quantum effects are provided.
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