Multifractal analysis for conformal graph directed Markov systems

Mario Roy; Mariusz Urbański

doi:10.3934/dcds.2009.25.627

Article Contents

2009, Volume 25, Issue 2: 627-650. Doi: 10.3934/dcds.2009.25.627

This issue Previous Article Asymptotic behavior of solutions of a free boundary problem modelling the growth of tumors with Stokes equations Next Article Structural stability of solutions to the Riemann problem for a scalar nonconvex CJ combustion model

Multifractal analysis for conformal graph directed Markov systems

Mario Roy^1, and
Mariusz Urbański^2,

1.
Glendon College, York University, 2275 Bayview Avenue, Toronto
2.
Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430

Received: October 2008

Revised: February 2009

Published: June 2009

Abstract / Introduction Related Papers Cited by

Abstract

We derive the multifractal analysis of the conformal measure (or, equivalently, of the invariant measure) associated to a family of weights imposed upon a graph directed Markov system (GDMS) using balls as the filtration. Our analysis is done over a subset of the limit set, a subset which is often large. In particular, this subset is the entire limit set when the GDMS under scrutiny satisfies a boundary separation condition. Our analysis also applies to more general situations such as real and complex continued fractions.

Keywords:

Mathematics Subject Classification: Primary: 28A80; Secondary: 37C45, 37D35.

Citation:

Article Metrics

HTML views() PDF downloads(87) Cited by(0)

Multifractal analysis for conformal graph directed Markov systems

Abstract

Access History

Article Metrics

Access History

Other Articles By Authors

Catalog

Multifractal analysis for conformal graph directed Markov systems

Abstract

Access History

SHARE

Article Metrics

Access History

Other Articles By Authors

Catalog

Export File

Citation

Format

Content