Brake orbits for Hamiltonian systems of classical type via Finsler\n geodesics

2021/11/11 by Dario Corona, Corona, Dario, Fabio Giannoni +1
Mathematics · Physics and Astronomy · #53B40 #58B20 #58E10 #70G75 #70H03 #Advanced Differential Geometry Research #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2111.06218

openalex publication_date 2021/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider Hamiltonian functions of classical type, namely even and convex\nwith respect to the generalized momenta. A brake orbit is a periodic solution\nof Hamilton's equations such that the generalized momenta are zero on two\ndifferent points. Under mild assumptions, this paper reduces the multiplicity\nproblem of the brake orbits for a Hamiltonian function of classical type to the\nmultiplicity problem of orthogonal geodesic chords in a concave Finslerian\nmanifold with boundary. This paper will be used for a generalization of a\nSeifert's conjecture about the multiplicity of brake orbits to Hamiltonian\nfunctions of classical type.\n

Citations

• Multiple orthogonal geodesic chords and a proof of Seifert's conjecture\n on brake orbits

Related

• Orthogonal Geodesic Chords, Brake Orbits and Homoclinic Orbits in Riemannian Manifolds
• Multiple orthogonal geodesic chords and a proof of Seifert's conjecture\n on brake orbits
• Multiple brake orbits in \mathbf m-dimensional disks
• Multiple orthogonal geodesic chords in nonconvex Riemannian disks using obstacles
• Bifurcation of closed orbits of Hamiltonian systems with application to geodesics of the Schwarzschild metric