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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


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
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 $ 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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Wei Cheng
Affiliation: Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China

PII: S 0002-9939(2010)10643-3
Keywords: Mather theory, $\alpha$-function, mechanical systems
Received by editor(s): December 30, 2009
Received by editor(s) in revised form: June 11, 2010
Published electronically: November 22, 2010
Additional Notes: This work was partially supported by the National Basic Research Program of China (Grant No. 2007CB814800) and Natural Scientific Foundation of China (Grant No. 10971093)
Communicated by: Yingfei Yi
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.