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Shrinking targets in parametrised families

Published online by Cambridge University Press:  28 November 2017

MAGNUS ASPENBERG  and
TOMAS PERSSON
MAGNUS ASPENBERG
Affiliation:
Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden. e-mail: magnusa@maths.lth.se, tomasp@maths.lth.se
TOMAS PERSSON
Affiliation:
Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden. e-mail: magnusa@maths.lth.se, tomasp@maths.lth.se
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Abstract

We consider certain parametrised families of piecewise expanding maps on the interval, and estimate and sometimes calculate the Hausdorff dimension of the set of parameters for which the orbit of a fixed point has a certain shrinking target property. This generalises several similar results for β-transformations to more general non-linear families. The proofs are based on a result by Schnellmann on typicality in parametrised families.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 2 , March 2019 , pp. 265 - 295
Copyright
Copyright © Cambridge Philosophical Society 2017 

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