کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4635856 | 1340715 | 2007 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Random dynamics of polynomials and devil's-staircase-like functions in the complex plane
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Random dynamics of polynomials and devil's-staircase-like functions in the complex plane Random dynamics of polynomials and devil's-staircase-like functions in the complex plane](/preview/png/4635856.png)
چکیده انگلیسی
Using the above result and combining it with the theory of random dynamics of complex polynomials, we consider the following: Let Ï be a Borel probability measure in the space {gâC[z]|deg(g)⩾2} with topology induced by the uniform convergence on the Riemann sphere C¯. We consider the i.i.d. random dynamics in C¯ such that at every step we choose a polynomial according to the distribution Ï. Let Tâ(z) be the probability of tending to ââC¯ starting from the initial value zâC¯ and let GÏ be the polynomial semigroup generated by the support of Ï. Suppose that the support of Ï is compact, the postcritical set of GÏ is bounded in the complex plane and the Julia set of GÏ is disconnected. Then, we show that (1) in each component U of the complement of the Julia set of GÏ, Tââ£U equals a constant CU, (2) Tâ:C¯â[0,1] is a continuous function on the whole C¯, and (3) if J1, J2 are two components of the Julia set of GÏ with J1 ⩽ J2, then maxzâJ1Tâ(z)⩽minzâJ2Tâ(z). Hence Tâ is similar to the devil's-staircase function.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 187, Issue 1, 1 April 2007, Pages 489-500
Journal: Applied Mathematics and Computation - Volume 187, Issue 1, 1 April 2007, Pages 489-500
نویسندگان
Hiroki Sumi,