Radial distribution of Julia sets of entire solutions to complex difference equations. (English) Zbl 1452.30018
Summary: In this paper, entire solutions \(f\) of a class of nonlinear difference equations are studied. By considering the order and deficiency of the coefficients in the equations, we investigate the properties of the radial distribution of the Julia set of \(f\), and estimate the lower bound of the measure of the set defined by the common limiting directions of Julia sets of shifts of \(f\).
MSC:
| 30D35 | Value distribution of meromorphic functions of one complex variable, Nevanlinna theory |
| 34M10 | Oscillation, growth of solutions to ordinary differential equations in the complex domain |
| 37F10 | Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets |
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