Axiom A polynomial skew products of ℂ2 and their postcritical sets
Axiom A polynomial skew products of ℂ2 and their postcritical sets
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Axiom A ℂ2 的多项式偏斜积及其后临界集
DOI：
10.1017/s0143385708000047
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发表时间：
2007
影响因子：
0.9
通讯作者：
Suzanne Lynch Hruska
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文献类型：
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作者：
Laura Demarco;Suzanne Lynch Hruska
一个多项式斜积是f（z，w）=（p（z），q（z，w））的映射，其中p和q是多项式，使得f全纯扩张到一个次数至少为2的自同态.对于多项式映射，双曲性等价于后临界集的闭包与Julia集不相交的条件;此外，临界点要么是吸引圈，要么是无穷大。对于多项式斜积，Jonsson [Dynamics of polynomial skew products on C2. Math.Ann.314（3）（1999），403-447]建立了f是公理A当且仅当后临界集的闭包与Julia集的右模拟不相交。在这里，我们提出了一个类似的结论：临界轨道要么逃逸到无穷大，要么积累在一个吸引集。此外，我们构建了公理A映射的新例子，展示了各种后临界行为。
Abstract A polynomial skew product of ℂ2 is a map of the form f(z,w)=(p(z),q(z,w)), where p and q are polynomials, such that f extends holomorphically to an endomorphism of ℙ2 of degree at least two. For polynomial maps of ℂ, hyperbolicity is equivalent to the condition that the closure of the postcritical set is disjoint from the Julia set; further, critical points either iterate to an attracting cycle or infinity. For polynomial skew products, Jonsson [Dynamics of polynomial skew products on C2. Math. Ann. 314(3) (1999), 403–447] established that f is Axiom A if and only if the closure of the postcritical set is disjoint from the right analog of the Julia set. Here we present an analogous conclusion: critical orbits either escape to infinity or accumulate on an attracting set. In addition, we construct new examples of Axiom A maps demonstrating various postcritical behaviors.
H. Sumi：“亚双曲和半双曲有理半群和斜积的动力学”Ergod & Dynam。
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