Three results on the regularity of the curves that are invariant by an exact symplectic twist map

DOI10.1007/s10240-009-0017-8zbMath1177.53070OpenAlexW2035926507WikidataQ124885712 ScholiaQ124885712MaRDI QIDQ1026656

Marie-Claude Arnaud

Publication date: 25 June 2009

Published in: Publications Mathématiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=PMIHES_2009__109__1_0/

zbMATH Keywords

symplectic twist mapLipschitz mapGreen bundle

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15)

Related Items (9)

Actions of symplectic homeomorphisms/diffeomorphisms on foliations by curves in dimension 2 ⋮ Limit sets of convex non-elastic billiards ⋮ Weak K. A. M. solutions and minimizing orbits of twist maps ⋮ Green bundles, Lyapunov exponents and regularity along the supports of the minimizing measures ⋮ The link between the shape of the irrational Aubry-Mather sets and their Lyapunov exponents ⋮ The non-hyperbolicity of irrational invariant curves for twist maps and all that follows ⋮ Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting ⋮ Non-differentiable irrational curves for twist map ⋮ On the accumulation of separatrices by invariant circles

Cites Work

• Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. (On smooth conjugacy of diffeomorphisms of the circle with rotations)
• Symplectic twist maps without conjugate points
• A theorem of E. Hopf
• Convex Hamiltonians without conjugate points
• A geometric proof of the existence of the Green bundles
• Unnamed Item
• Unnamed Item

This page was built for publication: Three results on the regularity of the curves that are invariant by an exact symplectic twist map