First Steps Towards a Symplectic Dynamics

Details First Steps Towards a Symplectic Dynamics First Steps Towards a Symplectic Dynamics

2011-02-18

arxiv.org/abs/1102.3723v1

Mathematics

Dynamical Systems

60 pages and 21 figures

Scientific paper

Many interesting physical systems have mathematical descriptions as finite-dimensional or infinite-dimensional Hamiltonian systems. Poincare who started the modern theory of dynamical systems and symplectic geometry developed a particular viewpoint combining geometric and dynamical systems ideas in the study of Hamiltonian systems. After Poincare the field of dynamical systems and the field of symplectic geometry developed separately. Both fields have rich theories and the time seems ripe to develop the common core with highly integrated ideas from both fields. We discuss problems which show how dynamical systems questions and symplectic ideas come together in a nontrivial way.

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