Work

Combinatorics of linear stability for Hamiltonian systems in arbitrary dimension

Year: 2024

Type: article

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 [7], 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.

Source: Mathematische Zeitschrift

DOI: 10.1007/s00209-024-03585-7

Authors: Agustin Moreno, Francesco Ruscelli

Institution: Heidelberg University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Deutsche Forschungsgemeinschaft, Universität Heidelberg, Air Force Office of Scientific Research