کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4666267 1345394 2012 68 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Combinatorics and topology of straightening maps, I: Compactness and bijectivity
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Combinatorics and topology of straightening maps, I: Compactness and bijectivity
چکیده انگلیسی

We study the parameter space structure of degree d≥3d≥3 one complex variable polynomials as dynamical systems acting on CC. We introduce and study straightening maps  . These maps are a natural higher degree generalization of the ones introduced by Douady and Hubbard to prove the existence of small copies of the Mandelbrot set inside itself. We establish that straightening maps are always injective and that their image contains all the corresponding hyperbolic systems. Also, we characterize straightening maps with compact domains. Moreover, we give two classes of bijective straightening maps. The first produces an infinite collection of embedded copies of the (d−1)(d−1)-fold product of the Mandelbrot set in the connectedness locus of degree d≥3d≥3. The second produces an infinite collection of full families of quadratic connected filled Julia sets in the cubic connectedness locus, such that each filled Julia set is quasiconformally embedded.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 231, Issue 5, 1 December 2012, Pages 2666–2733
نویسندگان
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