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# Article

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Keywords:
rational mapping; birational transformation; involutive transformation
Summary:
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.
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