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Daniel Massart

  1. Differentiability of Mather's beta function in low dimensions.

    Mon, 09/21/2009 - 13:59 — SomNambul
    Authors: Daniel Massart
    Subjects: Dynamical Systems
    Abstract

    Let $L$ be a time-periodic Tonelli Lagrangian on a closed manifold of
    dimension two. Then the $\beta$-function of $L$ is differentiable in at least
    $k$ directions at any $k$-irrational homology class. The same result holds when
    $L$ is an autonomous mechanical Lagrangian with a $C^3$ potential on a closed
    manifold of dimension three.

  2. Two remarks about Ma\~n\'e's conjecture.

    Mon, 09/21/2009 - 13:59 — SomNambul
    Authors: Daniel Massart
    Subjects: Dynamical Systems
    Abstract

    We prove that Ma\~n\'e's conjecture, as stated in {\em Lagrangian flows: the
    dynamics of globally minimizing orbits}, Bol. Soc. Brasil. Mat. (N.S.) 28
    (1997), no. 2, 141--153, contains another conjecture of Ma\~n\'e, stated in
    {\em Generic properties and problems of minimizing measures of Lagrangian
    systems} Nonlinearity 9 (1996) 273-310.

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