Bernoulli convolutions and 1D dynamics

Thomas Michael William Kempton; Tomas Persson

doi:10.1088/0951-7715/28/11/3921

Bernoulli convolutions and 1D dynamics

Thomas Michael William Kempton, Tomas Persson

Pure Mathematics

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

Abstract

We describe a family φ_λ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems φ_λand give some numerical evidence to suggest values of λ for which φ_λ may be piecewise convex.

Original language	English
Pages (from-to)	3921-3934
Journal	Nonlinearity
Volume	28
Issue number	11
DOIs	https://doi.org/10.1088/0951-7715/28/11/3921
Publication status	Published - 8 Oct 2015

Keywords

Bernoulli convolutions
1D dynamics
Ergodic theory
Transfer operators

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10.1088/0951-7715/28/11/3921

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© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at iopscience.iop.org / https://dx.doi.org/10.1088/0951-7715/28/11/3921
Accepted author manuscript, 260 KB

Non-conformal repellers: Fractal and multifractal structure of non-conformal repellers
Falconer, K. J. (PI)
EPSRC
13/01/14 → 12/01/17
Project: Standard

Cite this

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AB - We describe a family φλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems φλ and give some numerical evidence to suggest values of λ for which φλ may be piecewise convex.

KW - Bernoulli convolutions

KW - 1D dynamics

KW - Ergodic theory

KW - Transfer operators

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DO - 10.1088/0951-7715/28/11/3921

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Bernoulli convolutions and 1D dynamics

Abstract

Keywords

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Projects

Non-conformal repellers: Fractal and multifractal structure of non-conformal repellers

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