Closed curves on convex hypersurfaces and periods of nonlinear oscillations

DOI10.1007/BF01389167zbMath0471.70020OpenAlexW2011350060MaRDI QIDQ1157976

Christopher B. Croke, Alan Weinstein

Publication date: 1981

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142820

zbMATH Keywords

closed curves on convex hypersurfacesgeometric resultsnonlinear hamiltonian systems

Mathematics Subject Classification ID

Phase plane analysis, limit cycles for nonlinear problems in mechanics (70K05) Hamilton's equations (70H05)

Related Items (11)

Existence of multiple periodic orbits of Hamiltonian systems on positive-type hypersurfaces in \({\mathbb{R}}^{2n}\) ⋮ Regularity for stationary surfaces of constant mean curvature with free boundaries ⋮ Dynamical implications of convexity beyond dynamical convexity ⋮ Stationary minimal surfaces with boundary on a simplex ⋮ Dynamical convexity and elliptic periodic orbits for Reeb flows ⋮ Lusternik-Schnirelmann theory and closed Reeb orbits ⋮ Rigid constellations of closed Reeb orbits ⋮ Generalizations of Ekeland-Hofer and Hofer-Zehnder symplectic capacities and applications ⋮ Coisotropic Hofer-Zehnder capacities of convex domains and related results ⋮ Une théorie de Morse pour les systèmes hamiltoniens convexes ⋮ Stationary partitioning of convex bodies

Cites Work

• Poincaré's problem and the length of the shortest closed geodesic on a convex hypersurface
• The isoperimetric inequality
• Unnamed Item

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