On commuting Tonelli Hamiltonians: Autonomous case

2009/11/18 by Cui, Xiaojun, Li, Ji
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0911.3471

Abstract

We show that the Aubry sets, the Mañé sets, Mather's barrier functions are the same for two commuting autonomous Tonelli Hamiltonians. We also show the quasi-linearity of α-functions from the dynamical point of view and the existence of common C^1,1 critical subsolution for their associated Hamilton-Jacobi equations.

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