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Researchers study linear stability and bifurcations in Hamiltonian systems, using topological/combinatorial methods to refine the Krein–Moser theorem.

Table of Links

• Abstract
• Introduction
• Preliminaries
• The B-signature
• GIT sequence: low dimensions
• GIT sequence: arbitrary dimension
• Appendix A. Stability, the Krein–Moser theorem, and refinements and References

Abstract

We address the general problem of studying linear stability and bifurcations of periodic orbits for Hamiltonian systems of arbitrary degrees of freedom. We study the topology of the GIT sequence introduced by the first author and Urs frauenfelder in [FM], in arbitrary dimension. In particular, we note that the combinatorics encoding the linear stability of periodic orbits is governed by a quotient of the associahedron. Our approach gives a topological/combinatorial proof of the classical Krein–Moser theorem, and refines it for the case of symmetric orbits.