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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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.
  • Luis Barreira and Claudia Valls, Hölder Grobman-Hartman linearization, Discrete Contin. Dyn. Syst. 18 (2007), no. 1, 187–197. MR 2276493, DOI 10.3934/dcds.2007.18.187
  • G. R. Belitskii, On the Grobman-Hartman theorem in class $C^\alpha$. Unpublished preprint.
  • Patrick Bernard, Smooth critical sub-solutions of the Hamilton-Jacobi equation, Math. Res. Lett. 14 (2007), no. 3, 503–511. MR 2318653, DOI 10.4310/MRL.2007.v14.n3.a14
  • Patrick Bernard, Connecting orbits of time dependent Lagrangian systems, Ann. Inst. Fourier (Grenoble) 52 (2002), no. 5, 1533–1568 (English, with English and French summaries). MR 1935556
  • G. Contreras, R. Iturriaga, H. Sánchez-Morgado, Weak solutions of the Hamilton Jacobi equation for Time Periodic Lagrangians. Preprint. arXiv:1207.0287.
  • Renato Iturriaga and Héctor Sánchez-Morgado, Hyperbolicity and exponential convergence of the Lax-Oleinik semigroup, J. Differential Equations 246 (2009), no. 5, 1744–1753. MR 2494686, DOI 10.1016/j.jde.2008.12.012
  • Fathi A. The Weak KAM Theorem in Lagrangian Dynamics. To appear in Cambridge Studies in Advanced Mathematics.
  • E. Guerra and H. Sánchez-Morgado, Vanishing viscosity limits for space-time periodic Hamilton-Jacobi equations. Comm. Pure App. Analysis. 13 (2014) no. 1, 331-346. MR3082564.
  • John N. Mather, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z. 207 (1991), no. 2, 169–207. MR 1109661, DOI 10.1007/BF02571383
  • Kaizhi Wang and Jun Yan, The rate of convergence of new Lax-Oleinik type operators for time-periodic positive definite Lagrangian systems, Nonlinearity 25 (2012), no. 7, 2039–2057. MR 2947934, DOI 10.1088/0951-7715/25/7/2039
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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:
  • 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:
  • MathSciNet review: 3283659