Multifractal Spectrum for Barycentric Averages View Full Text


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Article Info

DATE

2016-10

AUTHORS

Alejandro Mesón, Fernando Vericat

ABSTRACT

Let X,ν and Y be a measured space and a CAT(0) space, respectively. If ℳ2(Y) is the set of measures on Y with finite second moment then a map bar:ℳ2(Y)→Y can be defined. Also, for any x∈X and for a map φ:X→Y, a sequence EN,φ(x) of empirical measures on Y can be introduced. The sequence barEN,φ(x) replaces in CAT(0) spaces the usual ergodic averages for real valuated maps. It converges in Y (to a map φ¯x) almost surely for any x∈X (Austin J Topol Anal. 2011;3: 145–152). In this work, we shall consider the following multifractal decomposition in X:Ky,φ=x:limN→∞barEN,φ(x)=y, and we will obtain a variational formula for this multifractal spectrum. More... »

PAGES

623-635

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10883-015-9278-3

DOI

http://dx.doi.org/10.1007/s10883-015-9278-3

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1027395034


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