The non-hyperbolicity of irrational invariant curves for twist maps and all that follows

DOI10.4171/RMI/917zbMath1361.37046arXiv1411.7072MaRDI QIDQ515352

Pierre Berger, Marie-Claude Arnaud

Publication date: 13 March 2017

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7072

zbMATH Keywords

Lyapunov exponentsinvariant curvesAubry-Mather theorysymplectic dynamicstwist mapsGreen bundlesGreene criterioninstability zones

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Dynamical aspects of twist maps (37E40)

Related Items (4)

A notion of Denjoy sub-system ⋮ The stable norm on the 2-torus at irrational directions ⋮ On Herman's positive entropy conjecture ⋮ On the marked length spectrum of generic strictly convex billiard tables

Cites Work

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• The discrete Frenkel-Kontorova model and its extensions: I. Exact results for the ground-states
• A nondifferentiable essential irrational invariant curve for a \(C^1\) symplectic twist map
• The link between the shape of the irrational Aubry-Mather sets and their Lyapunov exponents
• Three results on the regularity of the curves that are invariant by an exact symplectic twist map
• On the multiplicative ergodic theorem for uniquely ergodic systems
• Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting
• Boundaries of instability zones for symplectic twist maps

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