Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves

DOI10.4007/annals.2015.181.3.4zbMath1353.37090arXiv1204.4694OpenAlexW2127803340MaRDI QIDQ2349041

Barney Bramham

Publication date: 16 June 2015

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.4694

zbMATH Keywords

Hamiltonian systemsergodic theoryfoliationspseudoholomorphic curvesFloer theorypseudorotation

Mathematics Subject Classification ID

Symplectic aspects of Floer homology and cohomology (53D40) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Almost complex manifolds (32Q60) Pseudoholomorphic curves (32Q65)

Related Items

Hamiltonian pseudo-rotations of projective spaces, The Anosov-Katok method and pseudo-rotations in symplectic dynamics, Another look at the Hofer-Zehnder conjecture, On mixing diffeomorphisms of the disc, Contact three-manifolds with exactly two simple Reeb orbits, A finite dimensional proof of a result of Hutchings about irrational pseudo-rotations, \(C^0\)-gap between entropy-zero Hamiltonians and autonomous diffeomorphisms of surfaces, Pseudo-rotations and holomorphic curves, A finite dimensional approach to Bramham's approximation theorem, Pseudo-rotations with sufficiently Liouvillean rotation number are \(C^0\)-rigid, Pseudo-rotations and Steenrod squares, Pseudorotations of the -disc and Reeb flows on the -sphere

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A finite dimensional approach to Bramham's approximation theorem
• Intersection theory of punctured pseudoholomorphic curves
• Pseudo-rotations of the open annulus
• Strongly fillable contact manifolds and \(J\)-holomorphic foliations
• Compactness for embedded pseudoholomorphic curves in 3-manifolds
• Pseudo holomorphic curves in symplectic manifolds
• Generalizations of the Poincaré-Birkhoff theorem
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• The existence of minimal immersions of 2-spheres
• The dynamics on three-dimensional strictly convex energy surfaces
• Pseudoholomorphic curves in symplectizations with applications to the Weinstein conjecture in dimension three
• Finite energy foliations of tight three-spheres and Hamiltonian dynamics
• Compactness results in symplectic field theory
• Properties of pseudoholomorphic curves in symplectisations. I: Asymptotics
• The structure of branch points in minimal surfaces and in pseudoholomorphic curves
• Unlinked invariant sets of diffeomorphisms of the torus and the annulus
• Properties of pseudo-holomorphic curves in symplectisations. II: Embedding controls and algebraic invariants
• A characterisation of the tight three-sphere
• First steps in stable Hamiltonian topology
• Pseudo-rotations with sufficiently Liouvillean rotation number are \(C^0\)-rigid
• Automatic transversality and orbifolds of punctured holomorphic curves in dimension four
• Interior estimates for elliptic systems of partial differential equations
• The unregularized gradient flow of the symplectic action
• A characterization of the tight 3-sphere II
• Pseudo-rotations of the closed annulus: variation on a theorem of J Kwapisz
• Constructions in elliptic dynamics
• Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary