Hyperbolicity and exponential long-time convergence for space-time periodic Hamilton-Jacobi equations

In this note we prove exponential convergence to time-periodic states of the solutions of space-time periodic Hamilton-Jacobi equations, assuming that the Aubry set is the union of a finite number of hyperbolic periodic orbits of the Euler-Lagrange flow. The period of limiting solutions is the least...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2015-02, Vol.143 (2), p.731-740
Main Author: Héctor Sánchez-Morgado
Format: Article
Language:English
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Summary:In this note we prove exponential convergence to time-periodic states of the solutions of space-time periodic Hamilton-Jacobi equations, assuming that the Aubry set is the union of a finite number of hyperbolic periodic orbits of the Euler-Lagrange flow. The period of limiting solutions is the least common multiple of the periods of the orbits in the Aubry set. This extends a result that was obtained by Iturriaga and the author for the autonomous case.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-2014-12290-8