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Addressing the General Problem of Studying Linear Stability and Bifurcations of Periodic Orbitsby@graphtheory

Addressing the General Problem of Studying Linear Stability and Bifurcations of Periodic Orbits

by Graph TheoryJune 23rd, 2024
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Researchers study linear stability and bifurcations in Hamiltonian systems, using topological/combinatorial methods to refine the Krein–Moser theorem.
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Authors:

(1) Agustin Moreno;

(2) Francesco Ruscelli.

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.


This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license.