Smoothing Lyapunov functions

Fathi, Albert; Pageault, Pierre

doi:10.1090/tran/7329

Smoothing Lyapunov functions
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by Albert Fathi and Pierre Pageault PDF

Trans. Amer. Math. Soc. 371 (2019), 1677-1700 Request permission

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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