On commuting Tonelli Hamiltonians: Autonomous case

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 $\alpha$-functions from the dynamical point of view and the existence of common $C^{1,1}$ critical subsolution for their associated Hamilton-Jacobi equations.

15 pages

References in corpus (2)

• Weak KAM for commuting Hamiltonians
• On commuting Tonelli Hamiltonians: Time-periodic case

Cited by in corpus (1)

• Weak KAM for commuting Hamiltonians