Normal forms for symplectic matrices. (English) Zbl 1304.15012

Normal forms for symplectic matrices are constructed using elementary geometrical methods. They are expressed in terms of elementary Jordan matrices and integers with values in \(\{- 1,0,1\}\) related to signatures of quadratic forms naturally associated to the symplectic matrix. They are useful to give new characterisations of Conley-Zehnder indices of general paths of symplectic matrices. The natural interpretation of the signs appearing in the decomposition and the description of the decomposition for matrices with 1 as an eigenvalue are of interest in this description.


15A21 Canonical forms, reductions, classification
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