@article{Bandura_Savchuk_2021, title={Structure of the set of Borel exceptional vectors for entire curves. II}, volume={55}, url={http://matstud.org.ua/ojs/index.php/matstud/article/view/190}, DOI={10.30970/ms.55.2.137-145}, abstractNote={<p>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.<br>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<br>pairwise intersection of the subspaces contains only the zero vector. <br>A similar result is also valid for the set of Picard<br>exceptional vectors.<br>Another result shows that the structure of the set of Borel exceptional vectors for an entire curve of integer order<br>differs somewhat from the structure of such a set for an entire curve of non-integer order.<br>For a transcendental entire curve $\vec{G}:\mathbb{C}\to \mathbb{C}^{p}$ 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 $p-1$.</p> <p>However, the set of Picard exceptional vectors does not possess this property. We propose two examples of entire curves.<br>The first example shows the set of Borel exceptional vectors together with the zero vector for $p$-dimensional entire curve of integer order is<br>union of subspaces of dimension at most $p-1$ such that the total sum of these dimensions does not exceed $p$ and intersection of any pair of these subspaces contains only zero vector. The set of Picard exceptional vectors for the curve has the same property.<br>In the second example, we construct a $q$-dimensional entire curve of non-integer order for which the set of Borel exceptional vectors together with the zero vector is a subspace in $\mathbb{C}^{q}$ of dimension at most $q-1$ and the set of Picard exceptional vectors together with the zero vector<br>do not have the property. This set is a union of some subspaces.</p>}, number={2}, journal={Matematychni Studii}, author={Bandura, A.I. and Savchuk, Ya.I.}, year={2021}, month={Jun.}, pages={137-145} }