Abstract
Our objective is to determine which subsets of ℝd arise as escaping sets of continuous functions from ℝd 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.
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The second author was supported by Engineering and Physical Sciences Research Council grant EP/L019841/1.
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Short, I., Sixsmith, D.J. Escaping sets of continuous functions. JAMA 137, 875–896 (2019). https://doi.org/10.1007/s11854-019-0015-9
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DOI: https://doi.org/10.1007/s11854-019-0015-9