Actions of symplectic homeomorphisms/diffeomorphisms on foliations by curves in dimension 2

DOI10.1017/etds.2021.158OpenAlexW3096913012WikidataQ114118934 ScholiaQ114118934MaRDI QIDQ5889815

Maxime Zavidovique, Marie-Claude Arnaud

Publication date: 27 April 2023

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.01546

zbMATH Keywords

generating functionsintegrabilitytwist mapssymplectic homeomorphisms

Mathematics Subject Classification ID

Dynamical systems involving maps of the circle (37E10) Obstructions to integrability for finite-dimensional Hamiltonian and Lagrangian systems (nonintegrability criteria) (37J30) Dynamical aspects of twist maps (37E40) Symplectic and canonical mappings (37J11) Completely integrable discrete dynamical systems (37J70)

Related Items (2)

Weak K. A. M. solutions and minimizing orbits of twist maps ⋮ Polynomial entropy and polynomial torsion for fibered systems

Cites Work

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• Three results on the regularity of the curves that are invariant by an exact symplectic twist map
• The equality of mixed partial derivatives under weak differentiability conditions
• A necessary and sufficient condition for a twist map being integrable
• The group of Hamiltonian homeomorphisms and \(C^0\)-symplectic topology
• Differentiability of Mather's average action and integrability on closed surfaces
• A C^1 Arnol'd-Liouville theorem
• Diffeomorphisms and Volume-Preserving Embeddings of Noncompact Manifolds
• On global action-angle coordinates
• Torsion of instability zones for conservative twist maps on the annulus
• Hyperbolicity for conservative twist maps of the 2-dimensional annulus
• Invariant manifolds

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