Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting

DOI10.1017/S0143385712000065zbMath1269.37032arXiv1103.0194OpenAlexW2077176161MaRDI QIDQ4928746

Marie-Claude Arnaud

Publication date: 18 June 2013

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

Full work available at URL: https://arxiv.org/abs/1103.0194

zbMATH Keywords

Lyapunov exponentsTonelli Hamiltoniansminimizing measuresGreen bundlesconservative twist mapsOseledets' splitting

Mathematics Subject Classification ID

Related Items (5)

Lyapunov exponents of minimizing measures for globally positive diffeomorphisms in all dimensions ⋮ Hyperbolicity of minimizers and regularity of viscosity solutions for a random Hamilton-Jacobi equation ⋮ On the fragility of periodic tori for families of symplectic twist maps ⋮ The integrability of symplectic twist maps without conjugate points ⋮ The non-hyperbolicity of irrational invariant curves for twist maps and all that follows

Cites Work

• The link between the shape of the irrational Aubry-Mather sets and their Lyapunov exponents
• Action minimizing invariant measures for positive definite Lagrangian systems
• Green bundles and regularity of \(C^0\)-Lagrangians invariant graphs of Tonelli flows.
• Three results on the regularity of the curves that are invariant by an exact symplectic twist map
• On the entropy of the geodesic flow in manifolds without conjugate points
• 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

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