The Conley-Zehnder index for a path of symplectic matrices
Differential Geometry
2012-02-14 v2 Dynamical Systems
Symplectic Geometry
Abstract
We give here a self contained and elementary introduction to the Conley-Zehnder index for a path of symplectic matrices. We start from the definition of the index as the degree of a map into the circle for a path starting at the identity and ending at a matrix for which 1 is not an eigenvalue. We prove some properties which characterize this index using normal forms for symplectic matrices obtained from geometrical considerations. We explore the relations to Robbin-Salamon index for paths of Lagrangians. We give an axiomatic characterization of the generalization of the Conley-Zehnder index for any continuous path of symplectic matrices defined by Robbin and Salamon.
Keywords
Cite
@article{arxiv.1201.3728,
title = {The Conley-Zehnder index for a path of symplectic matrices},
author = {Jean Gutt},
journal= {arXiv preprint arXiv:1201.3728},
year = {2012}
}
Comments
60 pages, Refs added, prop 38 and corollaries 39, 40 added