Combinatorics of linear stability for Hamiltonian systems in arbitrary dimension

2023/11/10 by Agustín Moreno, Moreno, Agustin, Francesco Ruscelli +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2311.06167

openalex publication_date 2023/11/10 · openalex created_date 2023/11/14 · openalex updated_date 2026/07/28

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 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.

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