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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Smoothing Lyapunov functions


Authors: Albert Fathi and Pierre Pageault
Journal: Trans. Amer. Math. Soc. 371 (2019), 1677-1700
MSC (2010): Primary 37B25, 37C99
DOI: https://doi.org/10.1090/tran/7329
Published electronically: September 10, 2018
MathSciNet review: 3894031
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Abstract: We give a criterion for the approximation of a Lyapunov function by a smooth one. This improves results by F. Wesley Wilson obtained in 1969. We also show that we can obtain a smooth version of Conley's theorem on Lyapunov functions for flows, a fact that has been often claimed without proof.


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Additional Information

Albert Fathi
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 – and – ENS de Lyon (emeritus)
Email: albert.fathi@math.gatech.edu

Pierre Pageault
Affiliation: Lycée Etienne Mimard, 32 Rue Etienne Mimard, 42000 Saint-Étienne, France
Email: ppageault@gmail.com

DOI: https://doi.org/10.1090/tran/7329
Received by editor(s): October 5, 2016
Received by editor(s) in revised form: June 26, 2017
Published electronically: September 10, 2018
Additional Notes: This work was supported by ANR KAM faible (ANR-07-BLAN-0361-02) and ANR WKBHJ (ANR-12-BS01-0020).
Article copyright: © Copyright 2018 American Mathematical Society