On commuting Tonelli Hamiltonians: Autonomous case

Details On commuting Tonelli Hamiltonians: Autonomous case On commuting Tonelli Hamiltonians: Autonomous case

2009-11-18

arxiv.org/abs/0911.3471v2

Mathematics

Dynamical Systems

15 pages

Scientific paper

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 $\alpha$-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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