Pseudorandom numbers for conformal measures

Manfred Denker; Jinqiao Duan; Michael McCourt

doi:10.1080/14689360903002019

Pseudorandom numbers for conformal measures

Manfred Denker, Jinqiao Duan, Michael McCourt

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

2 Scopus citations

Abstract

We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Holder continuous potential φ : X → ℝ. In particular, we show that this algorithm provides good approximations to generic points for hyperbolic rational functions of degree two and the potential -h log |T'|, where h denotes the Hausdorff dimension of the Julia set of T.

Original language	English (US)
Pages (from-to)	439-457
Number of pages	19
Journal	Dynamical Systems
Volume	24
Issue number	4
DOIs	https://doi.org/10.1080/14689360903002019
State	Published - Dec 2009

All Science Journal Classification (ASJC) codes

General Mathematics
Computer Science Applications

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10.1080/14689360903002019

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title = "Pseudorandom numbers for conformal measures",

abstract = "We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Holder continuous potential φ : X → ℝ. In particular, we show that this algorithm provides good approximations to generic points for hyperbolic rational functions of degree two and the potential -h log |T'|, where h denotes the Hausdorff dimension of the Julia set of T.",

author = "Manfred Denker and Jinqiao Duan and Michael McCourt",

note = "Funding Information: This work was partly supported by the NSF Grant DMS-0620539. We would like to thank Xiaofan Li for helpful discussions in numerical error analysis. This work was partly done while J. Duan was a visiting professor at Universit{\"a}t G{\"o}ttingen and while M. Denker was a Distinguished Research Professor at Illinois Institute of Technology.",

year = "2009",

month = dec,

doi = "10.1080/14689360903002019",

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issn = "1468-9367",

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T1 - Pseudorandom numbers for conformal measures

AU - Denker, Manfred

AU - Duan, Jinqiao

AU - McCourt, Michael

N1 - Funding Information: This work was partly supported by the NSF Grant DMS-0620539. We would like to thank Xiaofan Li for helpful discussions in numerical error analysis. This work was partly done while J. Duan was a visiting professor at Universität Göttingen and while M. Denker was a Distinguished Research Professor at Illinois Institute of Technology.

PY - 2009/12

Y1 - 2009/12

N2 - We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Holder continuous potential φ : X → ℝ. In particular, we show that this algorithm provides good approximations to generic points for hyperbolic rational functions of degree two and the potential -h log |T'|, where h denotes the Hausdorff dimension of the Julia set of T.

AB - We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Holder continuous potential φ : X → ℝ. In particular, we show that this algorithm provides good approximations to generic points for hyperbolic rational functions of degree two and the potential -h log |T'|, where h denotes the Hausdorff dimension of the Julia set of T.

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U2 - 10.1080/14689360903002019

DO - 10.1080/14689360903002019

M3 - Article

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VL - 24

SP - 439

EP - 457

JO - Dynamical Systems

JF - Dynamical Systems

IS - 4

ER -

Pseudorandom numbers for conformal measures

Abstract

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