Shrinking targets in parametrised families
Dynamical Systems
2019-02-20 v2
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 -transformations to more general non-linear families. The proofs are based on a result by Schnellmann on typicality in parametrised families.
Cite
@article{arxiv.1603.01116,
title = {Shrinking targets in parametrised families},
author = {Magnus Aspenberg and Tomas Persson},
journal= {arXiv preprint arXiv:1603.01116},
year = {2019}
}
Comments
29 pages, 0 figures. Correction of the upper bound on the Hausdorff dimension, and some reorganisation of the paper