Aubry set on infinite cyclic coverings

DOI10.1134/s1560354723520015zbMath1527.37064OpenAlexW4385575508MaRDI QIDQ6069620

Pierre Pageault, Albert Fathi

Publication date: 14 November 2023

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1560354723520015

zbMATH Keywords

Aubry-Mather theoryweak KAM theoryinfinite cyclic coverings

Mathematics Subject Classification ID

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08) 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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• Action minimizing invariant measures for positive definite Lagrangian systems
• Weak KAM theorem on non compact manifolds
• Weak KAM from a PDE point of view: viscosity solutions of the Hamilton–Jacobi equation and Aubry set
• Recurrence on infinite cyclic coverings
• On the Hausdorff dimension of the mather quotient
• On the minimizing measures of Lagrangian dynamical systems
• Action-minimizing Methods in Hamiltonian Dynamics: An Introduction to Aubry-Mather Theory
• Lecture notes on Mather's theory for Lagrangian systems
• MATHER THEORY, WEAK KAM THEORY, AND VISCOSITY SOLUTIONS OF HAMILTON-JACOBI PDE'S

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