Stability of the Denjoy-Wolff theorem
| العنوان: | Stability of the Denjoy-Wolff theorem |
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| المؤلفون: | Ian Short, Argyrios Christodoulou |
| المصدر: | Annales Fennici Mathematici |
| بيانات النشر: | The Finnish Mathematical Society, 2021. |
| سنة النشر: | 2021 |
| مصطلحات موضوعية: | Physics, Mathematics - Complex Variables, Mathematics::Complex Variables, Holomorphic function, Mathematics::Classical Analysis and ODEs, Dynamical Systems (math.DS), Articles, hyperbolic metric, Combinatorics, Mathematics::Group Theory, holomorphic map, FOS: Mathematics, Mathematics - Dynamical Systems, Complex Variables (math.CV), Unit (ring theory), Denjoy-Wolff theorem |
| الوصف: | The Denjoy-Wolff theorem is a foundational result in complex dynamics, which describes the dynamical behaviour of the sequence of iterates of a holomorphic self-map $f$ of the unit disc $\mathbb{D}$. Far less well understood are nonautonomous dynamical systems $F_n=f_n\circ f_{n-1} \circ \dots \circ f_1$ and $G_n=g_1\circ g_{2} \circ \dots \circ g_n$, for $n=1,2,\dotsc$, where $f_i$ and $g_j$ are holomorphic self-maps of $\mathbb{D}$. Here we obtain a thorough understanding of such systems $(F_n)$ and $(G_n)$ under the assumptions that $f_n\to f$ and $g_n\to f$. We determine when the dynamics of $(F_n)$ and $(G_n)$ mirror that of $(f^n)$, as specified by the Denjoy-Wolff theorem, thereby providing insight into the stability of the Denjoy-Wolff theorem under perturbations of the map $f$. Comment: 10 pages, 1 figure |
| اللغة: | English |
| تدمد: | 2737-114X 2737-0690 |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b44984b09f7af95bb96987d5915c8fe5 https://afm.journal.fi/article/view/109594 |
| Rights: | OPEN |
| رقم الانضمام: | edsair.doi.dedup.....b44984b09f7af95bb96987d5915c8fe5 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 2737114X 27370690 |
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