Dynamically convex Finsler metrics and \(J\)-holomorphic embedding of asymptotic cylinders

DOI10.1007/s10455-008-9111-2zbMath1149.53045arXivmath/0701616OpenAlexW2008146095MaRDI QIDQ944920

Gabriel P. Paternain, Adam Harris

Publication date: 10 September 2008

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0701616

zbMATH Keywords

contact formFinsler metricdynamic convexity

Mathematics Subject Classification ID

Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds (58B20) Contact manifolds (general theory) (53D10) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60) Pseudoholomorphic curves (32Q65)

Related Items (19)

A generalized Poincaré-Birkhoff theorem ⋮ Elliptic bindings for dynamically convex Reeb flows on the real projective three-space ⋮ The existence of two closed geodesics on every Finsler 2-sphere ⋮ Symmetric periodic orbits and invariant disk-like global surfaces of section on the three-sphere ⋮ Dynamical convexity and elliptic periodic orbits for Reeb flows ⋮ Lusternik-Schnirelmann theory and closed Reeb orbits ⋮ A Hamiltonian version of a result of Gromoll and Grove ⋮ Dynamical systems. Abstracts from the workshop held July 11--17, 2021 (hybrid meeting) ⋮ The growth of the number of periodic orbits for annulus homeomorphisms and non-contractible closed geodesics on Riemannian or Finsler \(\mathbb{R} P^2\) ⋮ Reeb dynamics inspired by Katok's example in Finsler geometry ⋮ Some remarks on symmetric periodic orbits in the restricted three-body problem ⋮ The length of a shortest geodesic loop ⋮ Ergodicity and topological entropy of geodesic flows on surfaces ⋮ Global properties of tight Reeb flows with applications to Finsler geodesic flows on S² ⋮ Bumpy metrics on spheres and minimal index growth ⋮ Conformal great circle flows on the 3-sphere ⋮ The contact property for symplectic magnetic fields on ⋮ Magnetic Katok examples on the two-sphere ⋮ Open problems and questions about geodesics

Cites Work

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• The length of a shortest geodesic loop
• The dynamics on three-dimensional strictly convex energy surfaces
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• Projectively flat Finsler 2-spheres of constant curvature
• Singularities of \(J\)-holomorphic curves
• Finite energy foliations of tight three-spheres and Hamiltonian dynamics
• A sphere theorem for non-reversible Finsler metrics
• Zermelo navigation on Riemannian manifolds
• Two-dimensional Finsler metrics with constant flag curvature
• The existence of two closed geodesics on every Finsler 2-sphere
• ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS
• Geometry of the Katok examples
• C 2 densely the 2-sphere has an elliptic closed geodesic
• Branch structure of 𝐽–holomorphic curves near periodic orbits of a contact manifold

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