Combinatorics of linear stability for Hamiltonian systems in arbitrary dimension. On GIT quotients of the symplectic group, and the associahedron

DOI10.1007/S00209-024-03585-7MaRDI QIDQ6623318

Francesco Ruscelli, Agustin Moreno

Publication date: 23 October 2024

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

zbMATH Keywords

linear stabilitybifurcationperiodic orbitsymmetric orbitKrein-Moser theoremGIT sequence topology

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14) Periodic and almost periodic solutions for problems in Hamiltonian and Lagrangian mechanics (70H12)

Cites Work

• A fixed point theorem in symplectic geometry
• Linear stability of natural symplectic maps.
• Morse theory for Hamiltonian systems
• Stability of periodic orbits in the elliptic, restricted three-body problem.
• From Babylonian lunar observations to Floquet multipliers and Conley–Zehnder indices
• On doubly symmetric periodic orbits
• On GIT quotients of the symplectic group, stability and bifurcations of periodic orbits (with a view towards practical applications)
• Symplectic Methods in the Numerical Search of Orbits in Real-Life Planetary Systems
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