New minimal geodesics in the group of symplectic diffeomorphisms

DOI10.1007/BF01189394zbMath0828.58028OpenAlexW1991326932MaRDI QIDQ1894804

Karl Friedrich Siburg

Publication date: 26 July 1995

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01189394

zbMATH Keywords

Hamiltonian flowssymplectic diffeomorphismsHofer distanceminimal geodesics

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. I ⋮ Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. II ⋮ Bi-invariant metrics on the contactomorphism groups ⋮ Conjugate points on geodesics of Hofer's metric ⋮ Action spectrum and Hofer's distance between Lagrangian submanifolds. ⋮ Length minimizing Hamiltonian paths for symplectically aspherical manifolds. ⋮ Action-minimizing measures and the geometry of the Hamiltonian diffeomorphism group. ⋮ A sufficient minimality condition for geodesics of the Hofer's metric ⋮ Hofer-Zehnder capacity and length minimizing Hamiltonian paths ⋮ Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic sub\-manifolds

Cites Work

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• Geodesics of Hofer's metric on the group of Hamiltonian diffeomorphisms
• Estimates for the energy of a symplectic map
• The geometry of symplectic energy
• Geodesics in the compactly supported Hamiltonian diffeomorphism group
• Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. II
• On the topological properties of symplectic maps

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