Symplectic Geometry From A Dynamical Systems Point Of View
BibTeX
@MISC{Hofer_symplecticgeometry,
author = {H. Hofer},
title = {Symplectic Geometry From A Dynamical Systems Point Of View},
year = {}
}
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Abstract
hat M is a topological manifold of even dimension. An atlas A on M is said to be symplectic if the transition maps are symplectic as maps between open subsets of V . Two symplectic atlases are equivalent if the union is a symplectic atlas. A maximal symplectic atlas S is called a symplectic structure on M . For every chart ' we can define a closed two form of maximal rank ! ' = ' !. The collection f! ' g defines a global closed two-form ! S of maximal rank on M . In view of a result 1 2 H. HOFER due to Darboux an equivalent definition of a symplectic manifold is that of a smooth manifold M equipped with a closed two-form oe of maximal rank. Given a global symplectic diffeomorphism f : V !<F1
