Abstract: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.
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- Héctor Sánchez-Morgado
- Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México. México DF 04510, México
- MR Author ID: 340702
- ORCID: 0000-0003-3981-408X
- Email: firstname.lastname@example.org
- Received by editor(s): June 13, 2012
- Received by editor(s) in revised form: May 11, 2013
- Published electronically: October 22, 2014
- Communicated by: Walter Craig
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 143 (2015), 731-740
- MSC (2010): Primary 37J50, 49L25, 35F21; Secondary 70H20
- DOI: https://doi.org/10.1090/S0002-9939-2014-12290-8
- MathSciNet review: 3283659