Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. I

DOI10.1007/BF01231437zbMath0844.58020arXivmath/9503227MaRDI QIDQ1910204

François Lalonde, Dusa McDuff

Publication date: 25 August 1996

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

Full work available at URL: https://arxiv.org/abs/math/9503227

zbMATH Keywords

energystabilitygeodesicsHamiltonian symplectomorphismsHofer length functionalabsolutely length-minimizing

Mathematics Subject Classification ID

Geodesic flows in symplectic geometry and contact geometry (53D25) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items

Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. II, The Conley conjecture, Hofer's metric in compact Lie groups, Length minimizing Hamiltonian paths for symplectically aspherical manifolds., HAMILTONIAN FIELDS AND ENERGY IN CONTACT MANIFOLDS, A quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer's metric, Geodesics on the space of Lagrangian submanifolds in cotangent bundles, A MINIMAX SELECTOR FOR A CLASS OF HAMILTONIANS ON COTANGENT BUNDLES, Action-minimizing measures and the geometry of the Hamiltonian diffeomorphism group., Geodesics of Hofer's metric on the space of Lagrangian submanifolds, Gromov-Witten invariants and pseudo symplectic capacities, The positive fundamental group of Sp(2) and Sp(4), HOFER–ZEHNDER CAPACITY AND HAMILTONIAN CIRCLE ACTIONS, TOTALLY NON-COISOTROPIC DISPLACEMENT AND ITS APPLICATIONS TO HAMILTONIAN DYNAMICS, Metric geometry of infinite-dimensional Lie groups and their homogeneous spaces, Hamiltonian \(S^1\)-manifolds are uniruled, A COMPARISON OF HOFER'S METRICS ON HAMILTONIAN DIFFEOMORPHISMS AND LAGRANGIAN SUBMANIFOLDS, THE g-AREAS AND THE COMMUTATOR LENGTH, A relative Hofer estimate and the asymptotic Hofer-Lipschitz constant, Proof of the main conjecture on \(g\)-areas

Cites Work

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• Sur la structure du groupe des difféomorphismes qui preservent une forme symplectique
• 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
• Hofer's \(L^ \infty\)-geometry: Energy and stability of Hamiltonian flows. II
• Conjugate points on geodesics of Hofer's metric
• Symplectic displacement energy for Lagrangian submanifolds
• BIINVARIANT METRICS ON THE GROUP OF HAMILTONIAN DIFFEOMORPHISMS