Pseudo-rotations with sufficiently Liouvillean rotation number are \(C^0\)-rigid

DOI10.1007/s00222-014-0525-0zbMath1353.37007arXiv1205.6243OpenAlexW2004868504MaRDI QIDQ2257729

Barney Bramham

Publication date: 2 March 2015

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

Full work available at URL: https://arxiv.org/abs/1205.6243

zbMATH Keywords

symplectic diffeomorphismLiouville numbersFloer equationirrational pseudo-rotations

Mathematics Subject Classification ID

Related Items (14)

Hamiltonian pseudo-rotations of projective spaces ⋮ The Anosov-Katok method and pseudo-rotations in symplectic dynamics ⋮ Another look at the Hofer-Zehnder conjecture ⋮ Lusternik-Schnirelmann theory and closed Reeb orbits ⋮ On mixing diffeomorphisms of the disc ⋮ Mather's regions of instability for annulus diffeomorphisms ⋮ Pseudo-rotations and holomorphic curves ⋮ A finite dimensional approach to Bramham's approximation theorem ⋮ Pseudo-rotations and Steenrod squares ⋮ The rigidity of pseudo-rotations on the two-torus and a question of Norton-Sullivan ⋮ Approximate identities and Lagrangian Poincaré recurrence ⋮ Real-analytic AbC constructions on the torus ⋮ Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves ⋮ Pseudorotations of the -disc and Reeb flows on the -sphere

Cites Work

• Pseudo holomorphic curves in symplectic manifolds
• Some open problems in dynamical systems
• 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
• Ordinary differential equations. An introduction to nonlinear analysis. Transl. from the German by Gerhard Metzen
• First steps in stable Hamiltonian topology
• Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves
• Herman’s last geometric theorem
• CHARACTERISTIC LYAPUNOV EXPONENTS AND SMOOTH ERGODIC THEORY
• Constructions in elliptic dynamics
• Weak mixing disc and annulus diffeomorphisms with arbitrary Liouville rotation number on the boundary
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