Structure of the set of Borel exceptional vectors for entire curves. II - A.I. Bandura; Ya.I. Savchuk (Математичні Студії)
We have obtained a description of structure of the sets of Picard and Borel exceptional vectors for transcendental entire curve in some sense. We consider only $p$-dimensional entire curves with linearly independent components without common zeros. In particular, the set of Borel exceptional vectors together with the zero vector is a finite union of subspaces in $\mathbb{C}^{p}$ of dimension at most $p-1$. Moreover, the sum of their dimensions does not exceed $p$ if any pairwise intersection of the subspaces contains only the zero vector. A similar result is also valid for the set of Picard exceptional vectors. Another result shows that the structure of the set of Borel exceptional vectors for an entire curve of integer order differs somewhat from the structure of such a set for an entire curve of non-integer order. For a transcendental entire curve $\vec{G}:\mathbb{C}→ \mathbb{C}^{p}$ with linearly independent components and without common zeros having non-integer or zero order the set of Borel exceptional vectors together with the zero vector is a subspace in $\mathbb{C}^{p}$ of dimension at most $p-1$.