Divergence points of deformed empirical measures

L  Olsen

Divergence points of deformed empirical measures

L Olsen

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

We introduce and develope a unifying multifractal framework based on deformations of empirical measures. This framework (1) unifies and extends many results in multifractal analysis of local characteristics of dynamical systems and "fractal" measures and (2) provides a systematic basis for the detailed study of divergence points.

Original language	English
Pages (from-to)	701-713
Number of pages	13
Journal	Mathematical Research Letters
Volume	9
Issue number	5-6
Publication status	Published - Sept 2002

Keywords

fractals
multifractals
multifractal spectrum
local dimensions
spectrum of local Lyapunov exponents
spectrum of local entropies
spectrum of ergodic averages
empirical measures
divergence points
self-conformal sets
self-conformal measures
MULTIFRACTAL ANALYSIS
HAUSDORFF DIMENSION
LOCAL ENTROPIES
FRACTALS
GEOMETRY

Cite this

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AB - We introduce and develope a unifying multifractal framework based on deformations of empirical measures. This framework (1) unifies and extends many results in multifractal analysis of local characteristics of dynamical systems and "fractal" measures and (2) provides a systematic basis for the detailed study of divergence points.

KW - fractals

KW - multifractals

KW - multifractal spectrum

KW - local dimensions

KW - spectrum of local Lyapunov exponents

KW - spectrum of local entropies

KW - spectrum of ergodic averages

KW - empirical measures

KW - divergence points

KW - self-conformal sets

KW - self-conformal measures

KW - MULTIFRACTAL ANALYSIS

KW - HAUSDORFF DIMENSION

KW - LOCAL ENTROPIES

KW - FRACTALS

KW - GEOMETRY

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M3 - Article

SN - 1945-001X

VL - 9

SP - 701

EP - 713

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 5-6

ER -

Divergence points of deformed empirical measures

Abstract

Keywords

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