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arXiv · 0911.3471

On commuting Tonelli Hamiltonians: Autonomous case

Xiaojun Cui·Ji Li
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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 $\alpha$-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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Xiaojun Cui, Ji Li. 2009-11-18. On commuting Tonelli Hamiltonians: Autonomous case. https://arxiv.org/abs/0911.3471

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