Smooth complete Lyapunov functions for ODEs

Sigurdur Hafstein; Stefan Suhr

doi:10.1016/j.jmaa.2021.125003

Smooth complete Lyapunov functions for ODEs

Sigurdur Hafstein, Stefan Suhr

Faculty of Physical Sciences

University of Iceland

Research output: Contribution to journal › Article › peer-review

Abstract

We establish a link between complete Lyapunov functions in dynamical systems and time functions in general relativity. This result is the first converse theorem for smooth complete Lyapunov functions for general autonomous ODEs and a novel characterization of the chain recurrent set using cone fields.

Original language	English
Article number	125003
Journal	Journal of Mathematical Analysis and Applications
Volume	499
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2021.125003
Publication status	Published - 1 Jul 2021

Bibliographical note

Other keywords

Chain recurrent set
Dynamical system
Smooth complete Lyapunov function
Time function

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10.1016/j.jmaa.2021.125003

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title = "Smooth complete Lyapunov functions for ODEs",

abstract = "We establish a link between complete Lyapunov functions in dynamical systems and time functions in general relativity. This result is the first converse theorem for smooth complete Lyapunov functions for general autonomous ODEs and a novel characterization of the chain recurrent set using cone fields.",

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author = "Sigurdur Hafstein and Stefan Suhr",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

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doi = "10.1016/j.jmaa.2021.125003",

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AU - Suhr, Stefan

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N2 - We establish a link between complete Lyapunov functions in dynamical systems and time functions in general relativity. This result is the first converse theorem for smooth complete Lyapunov functions for general autonomous ODEs and a novel characterization of the chain recurrent set using cone fields.

AB - We establish a link between complete Lyapunov functions in dynamical systems and time functions in general relativity. This result is the first converse theorem for smooth complete Lyapunov functions for general autonomous ODEs and a novel characterization of the chain recurrent set using cone fields.

KW - Chain recurrent set

KW - Dynamical system

KW - Smooth complete Lyapunov function

KW - Time function

UR - https://www.scopus.com/pages/publications/85099820608

U2 - 10.1016/j.jmaa.2021.125003

DO - 10.1016/j.jmaa.2021.125003

M3 - Article

SN - 0022-247X

VL - 499

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

M1 - 125003

ER -

Smooth complete Lyapunov functions for ODEs

Abstract

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Other keywords

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