Abstract.
In this article, we prove different results concerning the regularity of the C 0-Lagrangian invariant graphs of the Tonelli flows. For example :
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in dimension 2 and in the autonomous generic case, we prove that such a graph is in fact C 1 on some set with (Lebesgue) full measure;
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under certain dynamical additional hypothesis, we prove that these graphs are C 1.
Résumé.
Dans cet article, on démontre différents résultats concernant la régularité des graphes C 0-lagrangiens invariants par des flots de Tonelli. Par exemple :
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en dimension 2, dans le cas autonome et générique, on montre que ces graphes sont de classe C 1 sur un ensemble de mesure (de Lebesque) pleine;
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sous certaines hypothèses concernant la dynamique restreinte, on montre que ces graphes sont de classe C 1.
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Communicated by Viviane Baladi.
Submitted: July 23, 2007. Accepted: February 14, 2008.
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Arnaud, MC. Fibrés de Green et Régularité des Graphes C 0-Lagrangiens Invariants par un Flot de Tonelli. Ann. Henri Poincaré 9, 881–926 (2008). https://doi.org/10.1007/s00023-008-0375-7
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DOI: https://doi.org/10.1007/s00023-008-0375-7