Cremer fixed points and small cycles
نویسندگان
چکیده
منابع مشابه
Cycles and Fixed Points of Happy Functions
Let N = {1, 2, 3, · · · } denote the natural numbers. Given integers e ≥ 1 and b ≥ 2, let x = ∑n i=0 aib i with 0 ≤ ai ≤ b − 1 (thus ai are the digits of x in base b). We define the happy function Se,b : N −→ N by
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It is shown that a polynomial with a Cremer periodic point has a non-accessible critical point in its Julia set provided that the Cremer periodic point is approximated by small cycles. Stony Brook IMS Preprint #1995/2 February 1995
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Abstract. This report consists of additions and corrections to the author’s paper [1], which appeared in the proceedings of the ANTS V conference. The work described here was presented at the conference itself, which took place after the original paper was published. The abstract of the original paper was as follows: We explore some questions related to one of Brizolis: does every prime p have ...
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A universal schema for diagonalization was popularized by N.S. Yanofsky (2003), based on a pioneering work of F.W. Lawvere (1969), in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function. It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema. Here, we fi...
متن کاملOn Biaccessible Points in the Julia Setof a Cremer Quadratic
We prove that the only possible biaccessible points in the Julia set of a Cremer quadraticpolynomialare the Cremer xed point and its preimages. This gives a partial answer to a question posed by C. McMullen on whether such a Julia set can contain any biaccessible point at all.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2004
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-04-03539-1