论文标题
驯服合理功能：迭代和轨道交叉点的分解
Tame rational functions: Decompositions of iterates and orbit intersections
论文作者
论文摘要
让$ a $在Riemann Sphere上至少有两个学位的合理功能。我们说，如果代数曲线$ a（x）-a（y）= 0 $没有零属或与对角线不同的因素，则$ a $是驯服的。在本文中，我们表明，如果温和的有理函数$ a $ a $ a $ a $ a $ a $具有无限交集的轨道，则$ a $ a $ and $ b $具有共同的迭代。我们还表明，对于驯服合理函数，$ a $ a $ a $ a $ a^{\ circ d}，$ $ $ d \ geq 1，$可以从单个迭代的$ a^{\ circ circ n}的分解中获得有理函数的组成，对于$ n $足够大。
Let $A$ be a rational function of degree at least two on the Riemann sphere. We say that $A$ is tame if the algebraic curve $A(x)-A(y)=0$ has no factors of genus zero or one distinct from the diagonal. In this paper, we show that if tame rational functions $A$ and $B$ have orbits with infinite intersection, then $A$ and $B$ have a common iterate. We also show that for a tame rational function $A$ decompositions of its iterates $A^{\circ d},$ $d\geq 1,$ into compositions of rational functions can be obtained from decompositions of a single iterate $A^{\circ N}$ for $N$ big enough.
