Eigenvaluations
Eigenvaluations
复制标题
特征值
DOI：
--
复制
发表时间：
2004
期刊：
影响因子：
--
通讯作者：
Mattias Jonsson
中科院分区：
文献类型：
--
作者：
C. Favre;Mattias Jonsson
研究了超吸引不动点芽和多项式映射在C^2中的动力学。在这两种情况下，我们证明了渐近吸引率是一个二次整数，并构造了一个具有充分不变性的多次谐波函数。这是通过找到一个无限近的点来实现的，在这个点上映射变成刚性的：临界集包含在一个有法线交叉的完全不变集合中。我们通过动力学在赋值空间上的诱导作用来定位这个无限近点。这个空间携带一个实数树结构，方便地编码局部数据：一个无限近点对应于树的一个开放子集。动作尊重树形结构，并承认一个不动点——或特征值——在某种意义上是吸引的。一个合适的吸引力盆地对应于所期望的无限近点。
We study the dynamics in C^2 of superattracting fixed point germs and of polynomial maps near infinity. In both cases we show that the asymptotic attraction rate is a quadratic integer, and construct a plurisubharmonic function with the adequate invariance property. This is done by finding an infinitely near point at which the map becomes rigid: the critical set is contained in a totally invariant set with normal crossings. We locate this infinitely near point through the induced action of the dynamics on a space of valuations. This space carries an real-tree structure and conveniently encodes local data: an infinitely near point corresponds to a open subset of the tree. The action respects the tree structure and admits a fixed point--or eigenvaluation--which is attracting in a certain sense. A suitable basin of attraction corresponds to the desired infinitely near point.