## The Orbits of Generalized Derivatives. (arXiv:1706.04111v1 [math.CV])

The infinitesimal space of a quasiregular mapping was introduced by
Gutlyanskii et al and generalized the idea of a derivative for this class of
mappings which is only differentiable almost everywhere. In this paper, we show
that the infinitesimal space is either simple, that is, it consists of only one
mapping, or it contains uncountable many. To achieve this, we define the orbit
of a given point as its image under all elements of the infinitesimal space. We
prove that this orbit is a compact and connected subset of $\mathbb{R}^n
\setminus \{ 0 \}$ and moreover, every such set can be realized as an orbit
space. We conclude with some examples exhibiting features of orbits.查看全文