Ledrappier–Young formulae for a family of nonlinear attractors

Lawrence David Lee; Natalia Anna Jurga

doi:10.1007/s00209-021-02876-7

Ledrappier–Young formulae for a family of nonlinear attractors

Lawrence David Lee, Natalia Anna Jurga

Pure Mathematics

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

Abstract

We study a natural class of invariant measures supported on the attractors of a family of nonlinear, non-conformal iterated function systems introduced by Falconer, Fraser and Lee. These are pushforward quasi-Bernoulli measures, a class which includes the well-known class of Gibbs measures for Hölder continuous potentials. We show that these measures are exact dimensional and that their exact dimensions satisfy a Ledrappier–Young formula.

Original language	English
Pages (from-to)	2413-2427
Number of pages	15
Journal	Mathematische Zeitschrift
Volume	300
Issue number	3
Early online date	4 Oct 2021
DOIs	https://doi.org/10.1007/s00209-021-02876-7
Publication status	Published - 1 Mar 2022

Keywords

Ledrappier–Young formula
Quasi-Bernoulli measure
Exact dimensional
Non-conformal attractor

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abstract = "We study a natural class of invariant measures supported on the attractors of a family of nonlinear, non-conformal iterated function systems introduced by Falconer, Fraser and Lee. These are pushforward quasi-Bernoulli measures, a class which includes the well-known class of Gibbs measures for H{\"o}lder continuous potentials. We show that these measures are exact dimensional and that their exact dimensions satisfy a Ledrappier–Young formula.",

keywords = "Ledrappier–Young formula, Quasi-Bernoulli measure, Exact dimensional, Non-conformal attractor",

author = "Lee, \{Lawrence David\} and Jurga, \{Natalia Anna\}",

note = "LDL was supported by an EPSRC Doctoral Training Grant (EP/N509759/1). NJ was supported by an EPSRC Standard Grant (EP/R015104/1). ",

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AU - Jurga, Natalia Anna

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N2 - We study a natural class of invariant measures supported on the attractors of a family of nonlinear, non-conformal iterated function systems introduced by Falconer, Fraser and Lee. These are pushforward quasi-Bernoulli measures, a class which includes the well-known class of Gibbs measures for Hölder continuous potentials. We show that these measures are exact dimensional and that their exact dimensions satisfy a Ledrappier–Young formula.

AB - We study a natural class of invariant measures supported on the attractors of a family of nonlinear, non-conformal iterated function systems introduced by Falconer, Fraser and Lee. These are pushforward quasi-Bernoulli measures, a class which includes the well-known class of Gibbs measures for Hölder continuous potentials. We show that these measures are exact dimensional and that their exact dimensions satisfy a Ledrappier–Young formula.

KW - Ledrappier–Young formula

KW - Quasi-Bernoulli measure

KW - Exact dimensional

KW - Non-conformal attractor

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DO - 10.1007/s00209-021-02876-7

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JF - Mathematische Zeitschrift

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Ledrappier–Young formulae for a family of nonlinear attractors

Abstract

Keywords

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Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Multifractal measures : from self-affine to nonlinear

Cite this

Ledrappier–Young formulae for a family of nonlinear attractors

Abstract

Keywords

Access to Document

Handle.net

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Fingerprint

Projects

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Student theses

Multifractal measures : from self-affine to nonlinear

Cite this