Линейно-инвариантные семейства отображений шара в $C^{N}$

In the paper we suggest a new definition of the order of a linearly invariant family of locally biholomorphic mappings of the unit ball in $\mathbb{C}^{n}$. This definition is equivalent to the one given by Pfaltzgraff in [1]. It bases on a very simple relationship with the Jacobian of the mappings (see Corollary 1). It appears that the order of a mapping depends only on its Jacobian (see Proposition 1).