对活动电流和分岔电流具有超吸引周期点的有理函数的均匀分布
Equidistribution of rational functions having a superattracting periodic point towards the activity current and the bifurcation current
摘要：
我们建立了具有标记临界点$c$的有理函数的全纯族$f$的参数空间中的活动电流$T_c$的近似，其中$c$在$f$下是周期性的，即，是一个超吸引周期点。这部分地推广了Dujardin-Favre定理的有理函数具有preperiodic点，并完善了Bassanelli-Berteloot定理的一个类似的近似的分歧电流$T_f$的全纯家庭$f$。证明是基于这种近似的动力学对应。
英文摘要：
We establish an approximation of the activity current $T_c$ in the parameter space of a holomorphic family $f$ of rational functions having a marked critical point $c$ by parameters for which $c$ is periodic under $f$, i.e., is a superattracting periodic point. This partly generalizes a Dujardin--Favre theorem for rational functions having preperiodic points, and refines a Bassanelli--Berteloot theorem on a similar approximation of the bifurcation current $T_f$ of the holomorphic family $f$. The proof is based on a dynamical counterpart of this approximation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
