标题： 割线映射的Böttcher型势 显示英文标题

标题： Böttcher-type potential for the secant map

摘要： 我们提出了一种用于割线法动力系统势能的Böttcher型全纯映射的构造，在根型不动点附近。 Böttcher型映射的模在不动点的吸引域上可以扩展为连续的，并且在不动点的迭代前像以外的地方是实解析的。 利用这个构造，我们证明了不动点的相关Green函数在其有限的区域是多调和的。 显示英文摘要

摘要： We present a construction of a B\"ottcher-type holomorphic map for the potential of the secant method dynamical system near a root-type fixed point. The modulus of the B\"ottcher-type map extends to be continuous on the entire basin of attraction of the fixed point, and is real-analytic away from the iterated preimages of the fixed point. Using this construction, we show the associated Green's function for the fixed point is pluriharmonic wherever it is finite.