多项式的时间平均
Time averages of polynomials
摘要：
我们定义并研究了多项式映射何时具有局部或全局时间平均。我们猜想复平面上的多项式f在点z附近有时间平均当且仅当z最终映射到f的Siegel圆盘上。我们证明了该猜想一般成立，即对于那些多项式的迭代具有最大数量的临界值。证明中的重要步骤依赖于对迭代单值群的理解。我们还证明了C^2的多项式自同构具有全局时间平均当且仅当映射与初等映射共轭。时间平均的定义是出于试图理解3维及更高维的多项式自同构群。
英文摘要：
We define and study when a polynomial mapping has a local or global time average. We conjecture that a polynomial f in the complex plane has a time average near a point z if and only if z is eventually mapped into a Siegel-disc of f. We prove that the conjecture holds generically, namely for those polynomials whose iterates have the maximal number of critical values. Important steps in the proofs rely on understanding the iterated monodromy groups. We also show that a polynomial automorphism of C^2 has a global time average if and only if the map is conjugate to an elementary mapping. The definition of a time average is motivated by an attempt to understand the polynomial automorphism groups in dimensions 3 and higher.
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