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

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 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. Authors: (1) Agustin Moreno; (2) Francesco Ruscelli. Authors: 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 Abstract Abstract Introduction Introduction Preliminaries Preliminaries The B-signature The B-signature GIT sequence: low dimensions GIT sequence: low dimensions GIT sequence: arbitrary dimension GIT sequence: arbitrary dimension Appendix A. Stability, the Krein–Moser theorem, and refinements and References 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. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. This paper is available on arxiv under CC BY-NC-SA 4.0 DEED license. available on arxiv