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Shrinking targets in parametrised families
Published online by Cambridge University Press: 28 November 2017
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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