Escaping sets of continuous functions
- 19 Downloads
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.
Unable to display preview. Download preview PDF.
- A. E. Eremenko, On the iteration of entire functions, in Dynamical Systems and Ergodic Theory (Warsaw 1986), Banach Center Publications, Vol. 23, PWN, Warsaw, 1989, pp. 339–345.Google Scholar
- M. Vuorinen, Conformal Geometry and Quasiregular Mappings, Lecture Notes in Mathematics, Vol. 1319, Springer-Verlag, Berlin, 1988.Google Scholar