Shrinking targets in parametrised families

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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.

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Subject classification (UKÄ) – MANDATORY

  • Geometry
Original languageEnglish
Pages (from-to)265-295
Number of pages31
JournalMathematical Proceedings of the Cambridge Philosophical Society
Volume166
Issue number2
Early online date2017 Nov 28
Publication statusPublished - 2019
Publication categoryResearch
Peer-reviewedYes