On the infinitesimal space of UQR mappings (Q524745)

The local behavior of a mapping \(f: G \to \mathbb{R}^n\), where \( G \subset \mathbb{R}^n\) is a domain, at a point \(x_0 \in G\) can be analysed in terms of the infinitesimal space \(T(x_0,f)\). If \(f\) is differentiable at \(x_0 \), then \(T(x_0,f)\) is a scaled version of the derivative. The authors study quasiregular maps \(f\) locally injective at a repelling or attracting fixed point \(x_0 \), and show that \(f\) may be conjugated to a uniformly quasiregular map \(g\) with fixed point \(0\) so that the infinitesimal space of \(g\) at \(0\) contains infinitely many elements. A map \(g\) is uniformly quasiregular if there exists \(K \geq 1\) such \(g\) and its iterates satisfy \(K(g^n)\leq K\), \(n=1,2,\dots \).