کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4668968 | 1346093 | 2014 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On multi-dimensional Fatou bifurcation
ترجمه فارسی عنوان
در دو بعد فاتو چند بعدی
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
چکیده انگلیسی
If f:(Cn,0)â(Cn,0) is a germ of a holomorphic map, such that zero is an isolated fixed point for all of its iterates, then by Nm(f) we denote the maximal number of periodic orbits of period m that can be born from the fixed point zero under a small perturbation of f. In [8] G.Y. Zhang (2007) proves that the linear part of a germ determines some natural restrictions on the possible sequences of numbers N1(f),N2(f),⦠(cf. Theorem 1.4). In this paper we show that when the linear part of f is diagonalizable, and all its eigenvalues are roots of unity of pairwise relatively prime degrees greater than 1, then in the case when n⩽2, there are no other restrictions on these sequences, except the ones given by the theorem of Zhang. We also show that this is not the case for n⩾3. In order to complete the proofs of these results, we establish an efficient way of computing the numbers Nm(f) for a large class of germs. An important tool that we use is the factor maps corresponding to the resonant normal forms.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 138, Issue 3, AprilâMay 2014, Pages 356-375
Journal: Bulletin des Sciences Mathématiques - Volume 138, Issue 3, AprilâMay 2014, Pages 356-375
نویسندگان
Igors Gorbovickis,