COMMUTING POLYNOMIALS AND POLYNOMIALS WITH SAME JULIA SET
نویسندگان
چکیده
منابع مشابه
Commuting Polynomials and Polynomials with Same Julia Set
It has been known since Julia that polynomials commuting under composition have the same Julia set. More recently in the works of Baker and Eremenko, Fernández, and Beardon, results were given on the converse question: When do two polynomials have the same Julia set? We give a complete answer to this question and show the exact relation between the two problems of polynomials with the same Juli...
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We prove that, with two exceptions, the set of polynomials with Julia set J has the form {σ pn : n ∈ N , σ ∈ Σ} , where p is one of these polynomials and Σ is the symmetry group of J . The exceptions occur when J is a circle or a straight line segment. Several papers [1, 2, 3, 5] have appeared dealing with the relation between polynomials having the same Julia set J (for notation the reader is ...
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Let F be an algebraically closed field of characteristic 0 and f(x) a polynomial of degree strictly greater than one in F [x]. We show that the number of degree k polynomials with coefficients in F that commute with f (under composition) is either zero or equal to the number of degree one polynomials with coefficients in F that commute with f . As a corollary, we obtain a theorem of E. A. Bertr...
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ژورنال
عنوان ژورنال: International Journal of Bifurcation and Chaos
سال: 1996
ISSN: 0218-1274,1793-6551
DOI: 10.1142/s0218127496001570