On the Hausdorff dimension of the Mather quotient

Creators: Fathi, Albert; Figalli, Alessio; Rifford, Ludovic

Others:: Department of Mathematics and Statistics [Texas Tech] ; Texas Tech University [Lubbock] (TTU); Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)

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Under appropriate assumptions on the dimension of the ambient manifold and the regularity of the Hamiltonian, we show that the Mather quotient is small in term of Hausdorff dimension. Then, we present applications in dynamics.

Abstract

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On the Hausdorff dimension of the Mather quotient

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Abstract

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