کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4630717 | 1340605 | 2012 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Continued fractions as dynamical systems
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The continued fraction expansion of a real number may be studied by considering a suitable discrete dynamical system of dimension two. In the special case where the number to be expanded is a quadratic irrational, that is a positive irrational root of a polynomial of degree two, more insight may be gained by considering a new dynamical system of dimension three, where the state vector stores the coefficients of the quadratic polynomials resulting from the expansion process. We show that a number of constants of motions can be derived and exploited to explore the attracting set of the solutions. Links with the solution to Pell’s equations are also investigated.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 218, Issue 16, 15 April 2012, Pages 8203–8216
Journal: Applied Mathematics and Computation - Volume 218, Issue 16, 15 April 2012, Pages 8203–8216
نویسندگان
Felice Iavernaro, Donato Trigiante,