Hyperbolicity and exponential convergence of the Lax-Oleinik semigroup

DOI10.1016/J.JDE.2008.12.012zbMath1163.37021OpenAlexW2017605818MaRDI QIDQ1007255

Héctor Sánchez-Morgado, Renato Iturriaga

Publication date: 20 March 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.12.012

zbMATH Keywords

periodic orbitsHamilton-Jacobi equationviscosity solutionsAubry setLax-Oleini semigroup

Mathematics Subject Classification ID

Hamilton-Jacobi equations in mechanics (70H20) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (8)

Exponential convergence to the stationary measure for a class of 1D Lagrangian systems with random forcing ⋮ Uniform exponential contraction for viscous Hamilton-Jacobi equations ⋮ Exponential convergence to time-periodic viscosity solutions in time-periodic Hamilton-Jacobi equations ⋮ Resonance conjecture via weak KAM theory ⋮ Exponential convergence of solutions for random Hamilton-Jacobi equations ⋮ A new kind of Lax-Oleinik type operator with parameters for time-periodic positive definite Lagrangian systems ⋮ The rate of convergence of the Lax-Oleinik semigroup-degenerate fixed point case ⋮ Hyperbolicity and exponential long-time convergence for space-time periodic Hamilton-Jacobi equations

Cites Work

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• Action minimizing invariant measures for positive definite Lagrangian systems
• Existence of \(C^1\) critical subsolutions of the Hamilton-Jacobi equation
• Smooth critical sub-solutions of the Hamilton-Jacobi equation
• Sur la convergence du semi-groupe de Lax-Oleinik
• Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens
• Lagrangian flows: The dynamics of globally minimizing orbits
• Action potential and weak KAM solutions

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