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

Author: Wei Cheng
Journal: Proc. Amer. Math. Soc. 139 (2011), 2143-2149
MSC (2010): Primary 37Jxx, 70Hxx
DOI: https://doi.org/10.1090/S0002-9939-2010-10643-3
Published electronically: November 22, 2010
MathSciNet review: 2775392
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Abstract: We study Mather's $\alpha$ -function for mechanical systems. We show that for mechanical systems, the $\alpha$ -function is differentiable at in at least one direction. We also give a topological condition on the potential function to guarantee the existence of a flat part near for general mechanical systems. Some examples are also given.

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