This article is cited in 4 papers

The growth of integral curves of finite lower order

V. P. Petrenko


Abstract: 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.
Bibliography: 31 titles.

UDC: 511.6+517.56

MSC: Primary 30A70; Secondary 30A64, 30A96

Received: 24.10.1973

 English version: Mathematics of the USSR-Sbornik, 1975, 26:4, 427–448

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