On shrinking targets for piecewise expanding interval maps

Tomas Persson; MICHAŁ RAMS

doi:10.1017/etds.2015.49

On shrinking targets for piecewise expanding interval maps

Tomas Persson, MICHAŁ RAMS

Institute - Center for Molecular and Macromolecular Studies of the Polish Academy of Sciences

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

Abstract

For a map (Formula presented.) with an invariant measure (Formula presented.), we study, for a (Formula presented.)-typical (Formula presented.), the set of points (Formula presented.) such that the inequality (Formula presented.) is satisfied for infinitely many (Formula presented.). We give a formula for the Hausdorff dimension of this set, under the assumption that (Formula presented.) is piecewise expanding and (Formula presented.) is a Gibbs measure. In some cases we also show that the set has a large intersection property.

Original language	English
Pages (from-to)	646-663
Journal	Ergodic Theory and Dynamical Systems
Volume	37
Issue number	02
Early online date	2015 Aug 25
DOIs	https://doi.org/10.1017/etds.2015.49
Publication status	Published - 2017 Apr

Subject classification (UKÄ)

Mathematics

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10.1017/etds.2015.49

https://arxiv.org/abs/1406.6785

Cite this

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title = "On shrinking targets for piecewise expanding interval maps",

abstract = "For a map (Formula presented.) with an invariant measure (Formula presented.), we study, for a (Formula presented.)-typical (Formula presented.), the set of points (Formula presented.) such that the inequality (Formula presented.) is satisfied for infinitely many (Formula presented.). We give a formula for the Hausdorff dimension of this set, under the assumption that (Formula presented.) is piecewise expanding and (Formula presented.) is a Gibbs measure. In some cases we also show that the set has a large intersection property.",

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year = "2017",

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AU - RAMS, MICHAŁ

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AB - For a map (Formula presented.) with an invariant measure (Formula presented.), we study, for a (Formula presented.)-typical (Formula presented.), the set of points (Formula presented.) such that the inequality (Formula presented.) is satisfied for infinitely many (Formula presented.). We give a formula for the Hausdorff dimension of this set, under the assumption that (Formula presented.) is piecewise expanding and (Formula presented.) is a Gibbs measure. In some cases we also show that the set has a large intersection property.

U2 - 10.1017/etds.2015.49

DO - 10.1017/etds.2015.49

M3 - Article

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SN - 1469-4417

VL - 37

SP - 646

EP - 663

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 02

ER -

On shrinking targets for piecewise expanding interval maps

Abstract

Subject classification (UKÄ)

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