Multifractal analysis for expanding interval maps with infinitely many branches

Ai-Hua Fan; Thomas M Jordan; Lingmin Liao; Michael Rams

doi:10.1090/S0002-9947-2014-06141-2

Multifractal analysis for expanding interval maps with infinitely many branches

Ai-Hua Fan, Thomas M Jordan, Lingmin Liao, Michael Rams

Research output: Contribution to journal › Article (Academic Journal) › peer-review

18 Citations (Scopus)

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Abstract

In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches.

Original language	English
Pages (from-to)	1847-1870
Number of pages	24
Journal	Transactions of the American Mathematical Society
Volume	367
Issue number	no. 3
DOIs	https://doi.org/10.1090/S0002-9947-2014-06141-2
Publication status	Published - Mar 2015

Keywords

Multifractal analysis
Birkhoff averages
interval maps
infinitely many branches

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10.1090/S0002-9947-2014-06141-2

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via AMS at http://www.ams.org/journals/tran/2015-367-03/S0002-9947-2014-06141-2/. Please refer to any applicable terms of use of the publisher.
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title = "Multifractal analysis for expanding interval maps with infinitely many branches",

abstract = "In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches.",

keywords = "Multifractal analysis, Birkhoff averages, interval maps, infinitely many branches",

author = "Ai-Hua Fan and Jordan, {Thomas M} and Lingmin Liao and Michael Rams",

year = "2015",

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T1 - Multifractal analysis for expanding interval maps with infinitely many branches

AU - Fan, Ai-Hua

AU - Jordan, Thomas M

AU - Liao, Lingmin

AU - Rams, Michael

PY - 2015/3

Y1 - 2015/3

N2 - In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches.

AB - In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this case and the setting where the expanding map has only finitely many branches.

KW - Multifractal analysis

KW - Birkhoff averages

KW - interval maps

KW - infinitely many branches

UR - http://arxiv.org/abs/1110.2856

U2 - 10.1090/S0002-9947-2014-06141-2

DO - 10.1090/S0002-9947-2014-06141-2

M3 - Article (Academic Journal)

SN - 0002-9947

VL - 367

SP - 1847

EP - 1870

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - no. 3

ER -

Multifractal analysis for expanding interval maps with infinitely many branches

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Dr Thomas M Jordan

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Multifractal analysis for expanding interval maps with infinitely many branches

Abstract

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Dr Thomas M Jordan

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