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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 $ 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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Additional Information

Wei Cheng
Affiliation: Department of Mathematics, Nanjing University, Nanjing, 210093, People’s Republic of China
Email: chengwei@nju.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-2010-10643-3
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.

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