A \({C^\infty}\) closing lemma for Hamiltonian diffeomorphisms of closed surfaces

DOI10.1007/s00039-016-0386-3zbMath1408.37092arXiv1512.06336OpenAlexW2964176436WikidataQ56697967 ScholiaQ56697967MaRDI QIDQ730358

Masayuki Asaoka, Kei Irie

Publication date: 27 December 2016

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.06336

zbMATH Keywords

Birkhoff normal formspectral invariantscontact homologyReeb flowsHamiltonian diffeomorphismsKAM invariant circles

Mathematics Subject Classification ID

Related Items (14)

Quantitative Heegaard Floer cohomology and the Calabi invariant ⋮ ECH capacities and the Ruelle invariant ⋮ \(C^r\)-closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle ⋮ On Herman's positive entropy conjecture ⋮ Feral curves and minimal sets ⋮ A finite dimensional proof of a result of Hutchings about irrational pseudo-rotations ⋮ Action and periodic orbits of area-preserving diffeomorphisms ⋮ On the generic Conley conjecture ⋮ Sub-leading asymptotics of ECH capacities ⋮ Floer homologies, with applications ⋮ Torsion contact forms in three dimensions have two or infinitely many Reeb orbits ⋮ The closing lemma and the planar general density theorem for Sobolev maps ⋮ Almost existence from the feral perspective and some questions ⋮ Homoclinic orbits for area preserving diffeomorphisms of surfaces

Cites Work

• Closing lemmas
• Quantitative embedded contact homology
• Area-preserving surface diffeomorphisms
• Dense existence of periodic Reeb orbits and ECH spectral invariants
• Proof of the Arnold conjecture for surfaces and generalizations to certain Kähler manifolds
• The dynamics on three-dimensional strictly convex energy surfaces
• Mathematical problems for the next century
• Mean action and the Calabi invariant
• Lectures on celestial mechanics. Transl. from the German by C. I. Kalme.
• Prime ends rotation numbers and periodic points
• The asymptotics of ECH capacities
• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
• The C¹ Closing Lemma, including Hamiltonians
• Regions of instability for non-twist maps
• The Closing Lemma
• An Improved Closing Lemma and a General Density Theorem
• From one Reeb orbit to two

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