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Combinatorics of linear stability for Hamiltonian systems in arbitrary dimension: The B-signature
Authors:
(1) Agustin Moreno;
(2) Francesco Ruscelli.
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
3. The B-signature
In this section, we discuss the notion of B-signature, or B-signs, introduced by the first author and Urs Frauenfelder in [FM], associated to a symmetric periodic orbit (see also [Ay22]).
Consider a Wonenburger matrix
The following result illustrates the uses of these signs, as they give information on the type of periodic orbit.
Theorem 2 ([FMb]). A symmetric periodic orbit of a Hamiltonian system with two degrees of freedom is negative hyperbolic if and only if its two B-signs are different.
This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license.
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