On Mather's -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 | References | Similar Articles | Additional Information

Abstract: We study Mather's -function for mechanical systems. We show that for mechanical systems, the -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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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.