The integrability of symplectic twist maps without conjugate points

DOI10.1017/etds.2019.49zbMath1457.37078arXiv1606.03132OpenAlexW2968715209WikidataQ127365670 ScholiaQ127365670MaRDI QIDQ5139069

Marc Arcostanzo

Publication date: 4 December 2020

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

Full work available at URL: https://arxiv.org/abs/1606.03132

zbMATH Keywords

complete integrabilitysymplectic twist mapweak KAM theory

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Canonical transformations in symplectic and contact geometry (53D22) Dynamical aspects of twist maps (37E40) Symplectic and canonical mappings (37J11) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Cites Work

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• Hopf rigidity for convex billiards on the hemisphere and hyperbolic plane
• On the geodesic flow of tori without conjugate points
• A necessary and sufficient condition for a twist map being integrable
• Symplectic twist maps without conjugate points
• Tonelli Hamiltonians without conjugate points and \(C^0\) integrability
• Minimizing orbits in the discrete Aubry–Mather model
• Converse KAM theory for symplectic twist maps
• Lower and upper bounds for the Lyapunov exponents of twisting dynamics: a relationship between the exponents and the angle of Oseledets’ splitting
• Variational Methods

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