The Polynomials Associated with a Julia Set
نویسندگان
چکیده
منابع مشابه
The Polynomials Associated With A Julia Set
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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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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In particular, the Julia set of z + c1 is locally connected if c1 ∈ [−2, 1/4] and totally disconnected if c1 ∈ R \ [−2, 1/4] (note that [−2, 1/4] is equal to the set of parameters c1 ∈ R for which the critical point c = 0 does not escape to infinity). This answers a question posed by Milnor, see [Mil1]. We should emphasize that if the ω-limit set ω(c) of the critical point c = 0 is not minimal ...
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In this paper, we obtain the dimensions of symmetry classes of polynomials associated with the irreducible characters of the dihedral group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes.
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 1995
ISSN: 0024-6093
DOI: 10.1112/blms/27.3.239