A symplectic proof of a theorem of Franks

DOI10.1112/S0010437X12000474zbMath1267.53093arXiv1107.1282MaRDI QIDQ4911993

Ely Kerman, Brian Collier, Andrew M. Zimmer, Bolor Turmunkh, Benjamin Reiniger

Publication date: 20 March 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.1282

zbMATH Keywords

periodic orbitsFloer homologyHamiltonian flowssymplectic topologydiffeomorphisms of \(S^2\)

Mathematics Subject Classification ID

Related Items (14)

Hamiltonian pseudo-rotations of projective spaces ⋮ On the Hofer–Zehnder conjecture on ℂPd via generating functions ⋮ Another look at the Hofer-Zehnder conjecture ⋮ Closed Reeb orbits on the sphere and symplectically degenerate maxima ⋮ On the Hofer-Zehnder conjecture ⋮ Contact three-manifolds with exactly two simple Reeb orbits ⋮ On periodic points of symplectomorphisms on surfaces ⋮ Hyperbolic fixed points and periodic orbits of Hamiltonian diffeomorphisms ⋮ The Conley conjecture and beyond ⋮ On reversible maps and symmetric periodic points ⋮ Perfect Reeb flows and action-index relations ⋮ On hyperbolic points and periodic orbits of symplectomorphisms ⋮ Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds ⋮ On the Hofer–Zehnder conjecture on weighted projective spaces

Cites Work

• The Conley conjecture for irrational symplectic manifolds
• The Conley conjecture
• Local Floer homology and the action gap
• Subharmonic solutions of Hamiltonian equations on tori
• Symplectic Floer homology of area-preserving surface diffeomorphisms
• Action and index spectra and periodic orbits in Hamiltonian dynamics
• Morse theory for Lagrangian intersections
• Geodesics on \(S^ 2\) and periodic points of annulus homeomorphisms
• Self-dual instantons and holomorphic curves
• Symplectic fixed points, the Calabi invariant and Novikov homology. [Appendix C in collaboration with Lê Tu Quôc Thang]
• \(\pi_1\) of symplectic automorphism groups and invertibles in quantum homology rings
• Periodic points of Hamiltonian surface diffeomorphisms
• Symplectic Floer homology and the mapping class group.
• Periodic orbits of Hamiltonian homeomorphisms of surfaces
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
• Constructions in elliptic dynamics

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