The ergodic theory of shrinking targets

Richard Hill; Sanju Velani

doi:10.1007/BF01245179

The ergodic theory of shrinking targets

Richard Hill, Sanju Velani

Mathematics

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

Abstract

To any dynamical system equipped with a metric, we associate a class of ldquowell approximablerdquo sets. In the case of an expanding rational map of the Riemann sphere acting on its Julia set, we estimate and in some cases compute the Hausdorff dimension of the associated ldquowell approximablerdquo sets. The methods used show a clear link between distortion properties and the type of results obtained in this paper, via ergodic theory and ubiquity.

Original language	English
Pages (from-to)	175-198
Number of pages	24
Journal	Inventiones mathematicae
Volume	119
Issue number	1
DOIs	https://doi.org/10.1007/BF01245179
Publication status	Published - Dec 1995

Keywords

Mathematik

Access to Document

10.1007/BF01245179

Cite this

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title = "The ergodic theory of shrinking targets",

abstract = "To any dynamical system equipped with a metric, we associate a class of ldquowell approximablerdquo sets. In the case of an expanding rational map of the Riemann sphere acting on its Julia set, we estimate and in some cases compute the Hausdorff dimension of the associated ldquowell approximablerdquo sets. The methods used show a clear link between distortion properties and the type of results obtained in this paper, via ergodic theory and ubiquity.",

keywords = " Mathematik",

author = "Richard Hill and Sanju Velani",

year = "1995",

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doi = "10.1007/BF01245179",

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T1 - The ergodic theory of shrinking targets

AU - Hill, Richard

AU - Velani, Sanju

PY - 1995/12

Y1 - 1995/12

N2 - To any dynamical system equipped with a metric, we associate a class of ldquowell approximablerdquo sets. In the case of an expanding rational map of the Riemann sphere acting on its Julia set, we estimate and in some cases compute the Hausdorff dimension of the associated ldquowell approximablerdquo sets. The methods used show a clear link between distortion properties and the type of results obtained in this paper, via ergodic theory and ubiquity.

AB - To any dynamical system equipped with a metric, we associate a class of ldquowell approximablerdquo sets. In the case of an expanding rational map of the Riemann sphere acting on its Julia set, we estimate and in some cases compute the Hausdorff dimension of the associated ldquowell approximablerdquo sets. The methods used show a clear link between distortion properties and the type of results obtained in this paper, via ergodic theory and ubiquity.

KW - Mathematik

U2 - 10.1007/BF01245179

DO - 10.1007/BF01245179

M3 - Article

VL - 119

SP - 175

EP - 198

JO - Inventiones mathematicae

JF - Inventiones mathematicae

IS - 1

ER -