特征值
Eigenvaluations
摘要：
我们研究了C^2中超吸引不动点芽和无穷远点附近多项式映射的动力学。在这两种情况下，我们证明了渐近吸引率是一个二次整数，并构造了一个多重次调和函数具有足够的不变性。这是通过找到一个无限接近的点，在那里地图成为刚性：临界集包含在一个完全不变的集与正规交叉。我们通过动力学在估值空间上的诱导作用来定位这个无穷近点。这个空间具有实树结构，并方便地编码本地数据：无限近点对应于树的开子集。这个动作尊重树结构，并承认一个不动点--或特征值--在某种意义上是吸引的。合适的吸引区域对应于所需的无限近点。
英文摘要：
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.
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