The Anosov-Katok method and pseudo-rotations in symplectic dynamics

DOI10.1007/s11784-022-00955-8zbMath1501.37058arXiv2010.06237OpenAlexW3093268645MaRDI QIDQ2139550

Frédéric Le Roux, Sobhan Seyfaddini

Publication date: 18 May 2022

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.06237

zbMATH Keywords

unique ergodicitysymplectic dynamicsAnosov-Katok methodpseudo rotations

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Symplectic manifolds (general theory) (53D05) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Rotation numbers and vectors (37E45) Dynamical systems involving smooth mappings and diffeomorphisms (37C05) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (2)

Another look at the Hofer-Zehnder conjecture ⋮ Contact three-manifolds with exactly two simple Reeb orbits

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A finite dimensional approach to Bramham's approximation theorem
• The Conley conjecture
• Subharmonic solutions of Hamiltonian equations on tori
• Pseudo-rotations of the open annulus
• Floer-Novikov cohomology and the flux conjecture
• Symplectic topology and Hamiltonian dynamics
• Generalizations of the Poincaré-Birkhoff theorem
• Convexity properties of the moment mapping
• Hamiltonian loops from the ergodic point of view
• Moment maps and combinatorial invariants of Hamiltonian \(T^ n\)-spaces
• Hamiltonian pseudo-rotations of projective spaces
• The conjugation method in symplectic dynamics
• An extension theorem in symplectic geometry
• Torus actions on symplectic manifolds
• Pseudo-rotations and Steenrod squares
• Pseudo-rotations and Steenrod squares revisited
• On mixing diffeomorphisms of the disc
• Pseudo-rotations with sufficiently Liouvillean rotation number are \(C^0\)-rigid
• Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves
• Periodic orbits of Hamiltonian homeomorphisms of surfaces
• Convexity and Commuting Hamiltonians
• ERGODIC PERTURBATIONS OF DEGENERATE INTEGRABLE HAMILTONIAN SYSTEMS
• Pseudo-rotations of the closed annulus: variation on a theorem of J Kwapisz
• Constructions in elliptic dynamics

This page was built for publication: The Anosov-Katok method and pseudo-rotations in symplectic dynamics