On the Hausdorff Dimension of the Mather Quotient

2007/11/08 by Fathi, Albert, Figalli, Alessio, Rifford, Ludovic · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.0711.1359

Abstract

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.

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