On commuting Tonelli Hamiltonians: Autonomous case
Abstract
We show that the Aubry sets, the Ma\~n\'e 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 C1,1 critical subsolution for their associated Hamilton-Jacobi equations.
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