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On the Hausdorff dimension of the mather quotient
Author(s) -
Fathi Albert,
Rifford Ludovic,
Figalli Alessio
Publication year - 2009
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20250
Subject(s) - hausdorff dimension , quotient , dimension (graph theory) , hausdorff space , mathematics , pure mathematics , effective dimension , hausdorff measure
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 the Hausdorff dimension. Then we present applications in dynamics. © 2008 Wiley Periodicals, Inc.