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
Full-text PDF Free Access
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.