Escaping sets of continuous functions

Short, Ian and Sixsmith, David J ORCID: 0000-0002-3543-6969 (2019) Escaping sets of continuous functions. JOURNAL D ANALYSE MATHEMATIQUE, 137 (2). pp. 875-896.

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Official URL: http://dx.doi.org/10.1007/s11854-019-0015-9

Abstract

Our objective is to determine which subsets of $\mathbb{R}^d$ arise as escaping sets of continuous functions from $\mathbb{R}^d$ to itself. We obtain partial answers to this problem, particularly in one dimension, and in the case of open sets. We give a number of examples to show that the situation in one dimension is quite different from the situation in higher dimensions. Our results demonstrate that this problem is both interesting and perhaps surprisingly complicated.

Item Type:	Article
Additional Information:	Accepted for publication by J. Anal. Math
Uncontrolled Keywords:	math.DS, math.DS
Depositing User:	Symplectic Admin
Date Deposited:	11 Apr 2017 10:36
Last Modified:	19 Jan 2023 07:06
DOI:	10.1007/s11854-019-0015-9
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3006835