庞加莱函数的复渐近性与朱利亚集的性质
Complex asymptotics of Poincaré functions and properties of Julia sets
摘要：
研究了Poincaré函数方程$f(λz)=p(f(z))$（$λ>1$）解的渐近性态，其中$p$是一个实的$\geq2$次多项式.发生的周期函数的恒定性的特点是在$p$的朱利亚集的几何性质。对于实朱利亚集，给出了Pommerenke-Levin-Yoccoz型乘子的不等式. $f$的零点分布与$p$的朱利亚集上的调和测度有关。
英文摘要：
The asymptotic behaviour of the solutions of Poincaré's functional equation $f(λz)=p(f(z))$ ($λ>1$) for $p$ a real polynomial of degree $\geq2$ is studied in angular regions of the complex plain. The constancy of an occurring periodic function is characterised in terms of geometric properties of the Julia set of $p$. For real Julia sets we give inequalities for multipliers of Pommerenke-Levin-Yoccoz type. The distribution of zeros of $f$ is related to the harmonic measure on the Julia set of $p$.
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