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Communications on Pure and Applied Mathematics
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On the Hausdorff dimension of the mather quotient

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 28 Mar 2008Embargo end date: 01 Jan 2007 English Publisher:WileyJournal:Communications on Pure and Applied Mathematics, volume 62, pages 445-500 (issn: 0010-3640, eissn: 1097-0312, Copyright policy )
Authors: Fathi, Albert; Figalli, Alessio; Rifford, Ludovic;

doi: 10.1002/cpa.20250 , 10.48550/arxiv.0711.1359

arXiv: http://arxiv.org/abs/0711.1359

On the Hausdorff dimension of the mather quotient

Abstract

AbstractUnder 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.

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Keywords

FOS: Mathematics, [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Dynamical Systems (math.DS), [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Dynamical Systems

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    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    		 Top 10%
    influence
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
28
Top 10%
Top 10%
Top 10%
Green
bronze