The growth of integral curves of finite lower order

The paper is concerned with the study of the deviations of integral curves of finite lower order.
The basic result is that if a $p$-dimensional integral curve $\mathbf G(z)$ has finite lower order $\lambda,$ then its deviations with respect to an arbitrary fixed admissible system of vectors $A$ satisfy
$$ \sum_{a\in A}\beta(a,\mathbf G)\leqslant K(1+\lambda)(p!)^3, $$
where $K$ is an absolute constant.
This estimate is an analogue of the classical relation for the defects of integral curves.
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