On Mather’s 𝛼-function of mechanical systems

Cheng, Wei

doi:10.1090/S0002-9939-2010-10643-3

On Mather’s $\alpha$-function of mechanical systems
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Proc. Amer. Math. Soc. 139 (2011), 2143-2149 Request permission

Abstract:

We study Mather’s $\alpha$-function for mechanical systems. We show that for mechanical systems, the $\alpha$-function is differentiable at $c=0$ in at least one direction. We also give a topological condition on the potential function to guarantee the existence of a flat part near $c=0$ for general mechanical systems. Some examples are also given.

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