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Proceedings of the American Mathematical Society

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ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Hyperbolicity and exponential long-time convergence for space-time periodic Hamilton-Jacobi equations
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by Héctor Sánchez-Morgado PDF
Proc. Amer. Math. Soc. 143 (2015), 731-740 Request permission

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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Additional Information
  • 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: hector@math.unam.mx
  • 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