Axiom A polynomial skew products of C^2 and their postcritical sets - Mathematics Dynamical SystemsReport as inadecuate




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Abstract: A polynomial skew product of C^2 is a map of the form fz,w = pz,qz,w, where p and q are polynomials, such that f is regular of degree d >=2. For polynomial maps of C, hyperbolicity is equivalent to the condition thatthe closure of the postcritical set is disjoint from the Julia set; further,critical points either iterate to an attracting cycle or infinity. Forpolynomial skew products, Jonsson Math. Ann., 1999 established that f isAxiom A if and only if the closure of the postcritical set is disjoint from theright analog of the Julia set. Here we present the 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 variouspostcritical behaviors.



Author: Laura DeMarco, Suzanne Lynch Hruska

Source: https://arxiv.org/







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