Perturbation Theory for Viscosity Solutions of Hamilton--Jacobi Equations and Stability of Aubry--Mather Sets

DOI10.1137/S0036141002405960zbMath1034.37035MaRDI QIDQ4429879

Diogo Aguiar Gomes

Publication date: 30 September 2003

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

controlasymptotic expansionKAM theoryAubry-Mather setsHamiltonian dynamicsviscosity solutions

Mathematics Subject Classification ID

Asymptotic expansions of solutions to PDEs (35C20) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (9)

Some inverse problems in periodic homogenization of Hamilton-Jacobi equations ⋮ An infinite-dimensional weak KAM theory via random variables ⋮ Weak KAM theory for discounted Hamilton-Jacobi equations and its application ⋮ Filling times for linear flow on the torus with truncated Diophantine conditions: a brief review and new proof ⋮ Viscosity solutions methods for converse KAM theory ⋮ Regularity of viscosity solutions near KAM torus ⋮ Viscous stability of quasi-periodic tori ⋮ Strong stability of KAM tori: From the point of view of viscosity solutions of H-J equations ⋮ Perturbation estimates of weak KAM solutions and minimal invariant sets for nearly integrable Hamiltonian systems

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