Conjugate points on geodesics of Hofer's metric

DOI10.1016/S0926-2245(96)00027-7zbMath0864.58004WikidataQ115337653 ScholiaQ115337653MaRDI QIDQ1924848

Ilya Ustilovsky

Publication date: 26 May 1997

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

zbMATH Keywords

second variationsymplectic manifoldHofer metricFinslerian geometryHamiltonian diffeomorphisms

Mathematics Subject Classification ID

Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items

Geodesics of Hofer's metric on the group of Hamiltonian diffeomorphisms, Local non-squeezing theorems and stability, Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. I, Bi-invariant metrics on the contactomorphism groups, Geodesics of norms on the contactomorphisms group of \(\mathbb{R}^{2n}\times S^1\), Action spectrum and Hofer's distance between Lagrangian submanifolds., Length minimizing Hamiltonian paths for symplectically aspherical manifolds., Geodesics of Hofer's metric on the space of Lagrangian submanifolds, Quantum characteristic classes and the Hofer metric, Morse theory for the Hofer length functional, The coadjoint operator, conjugate points, and the stability of ideal fluids, Symplectic topology in the nineties, Hofer-Zehnder capacity and length minimizing Hamiltonian paths, Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic sub\-manifolds, Fredholm properties of the \(L^2\) exponential map on the symplectomorphism group

Cites Work

• Geodesics of Hofer's metric on the group of Hamiltonian diffeomorphisms
• Estimates for the energy of a symplectic map
• The geometry of symplectic energy
• New minimal geodesics in the group of symplectic diffeomorphisms
• Local non-squeezing theorems and stability
• On the topological properties of symplectic maps
• Unnamed Item
• Unnamed Item
• Unnamed Item