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On polynomials having different types of iterative roots. (English) Zbl 1038.12500

Mira, Ch. (ed.) et al., Iteration theory. Proceedings of the 7th European conference, ECIT ’89, Batschuns, Austria, September 10–16, 1989. Singapore: World Scientific (ISBN 981-02-0611-9/hbk). 315-319 (1991).
Summary: In this paper several examples are given illustrating different situations with respect to iterative roots. It is shown that there are polynomials which have polynomial roots of order \(n\) and also roots of order \(n\) in the class of non terminating power series. Furthermore an example of a polynomial is provided having no polynomial as \(n\)th root, but having a nonterminating power series as an \(n\)th root as well as a phantom root of that order.
For the entire collection see [Zbl 0984.00044].

MSC:

12D10 Polynomials in real and complex fields: location of zeros (algebraic theorems)
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