论文标题
弱化后有限的周期性一直沿着地图往下缩
Periodic points of weakly post-critically finite all the way down maps
论文作者
论文摘要
我们研究了$ \ mathbb {cp}^n $在较高维度的$ \ mathbb {cp}^n $的经过定期周期的特征值。当$ n = 1 $这些值是$ 0 $或模量严格大于$ 1 $时，这是一个经典的结果。它是在[van tu le中猜想的。后代数霍明型内态的周期性点，千古理论和动态系统，第1-33、2020页，每个$ n \ geq 2 $。在本文中，我们验证了在[Matthieu Astorg，在高维理论和动力学系统中的批判后有限图的动力学，40（2）：289-308，2020]中引入的弱化后有限的疑虑。该类包含[Sarah Koch，Teichmüller理论和准确有限的内态性，数学进展，248：573-617，2013]中的一类著名的后有限地图。结果，我们验证了Koch地图的猜想。
We study eigenvalues along periodic cycles of post-critically finite endomorphisms of $\mathbb{CP}^n$ in higher dimension. It is a classical result when $n = 1$ that those values are either $0$ or of modulus strictly bigger than $1$. It has been conjectured in [Van Tu Le. Periodic points of post-critically algebraic holomorphic endomorphisms, Ergodic Theory and Dynamical Systems, pages 1-33, 2020] that the same result holds for every $n \geq 2$. In this article, we verify the conjecture for the class of weakly post-critically finite all the way down maps which was introduced in [Matthieu Astorg, Dynamics of post-critically finite maps in higher dimension, Ergodic Theory and Dynamical Systems, 40(2):289-308, 2020]. This class contains a well-known class of post-critically finite maps constructed in [Sarah Koch, Teichmüller theory and critically finite endomorphisms, Advances in Mathematics, 248:573-617, 2013]. As a consequence, we verify the conjecture for Koch maps.
