## Zdeněk Dušek, Oldřich Kowalski

*Involutive birational transformations of~arbitrary complexity in Euclidean spaces*

Comment.Math.Univ.Carolin. 54,1 (2013) 111-117.**Abstract:**A broad family of involutive birational transformations of an open dense subset of $\mathbb R^n$ onto itself is constructed explicitly. Examples with arbitrarily high complexity are presented. Construction of birational transformations such that $\phi^k= \mathrm{Id}$ for a fixed integer $k>2$ is also presented.

**Keywords:** rational mapping, birational transformation, involutive transformation

**AMS Subject Classification:** 14E05

PDF