p-Adic (3, 2)-rational dynamical systems

We investigate behavior of trajectory of a (3, 2)-rational p -adic dynamical system in complex p -adic field . The paper studies Siegel disks and attractors of these dynamical systems. The set of fixed points of the (3, 2)-rational function may by empty, or may consist of a single element, or of two...

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Bibliographic Details
Published in:P-adic numbers, ultrametric analysis, and applications ultrametric analysis, and applications, 2015, Vol.7 (1), p.39-55
Main Author: Sattarov, I. A.
Format: Article
Language:English
Subjects:
Algebra
Mathematics
Mathematics and Statistics
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Summary:We investigate behavior of trajectory of a (3, 2)-rational p -adic dynamical system in complex p -adic field . The paper studies Siegel disks and attractors of these dynamical systems. The set of fixed points of the (3, 2)-rational function may by empty, or may consist of a single element, or of two elements. We obtained the following results. In the case of existence of two fixed points, the p -adic dynamical system has a very rich behavior: we show that Siegel disks may either coincide or be disjoint for different fixed points of the dynamical system. Besides, we find the basin of the attractor of the system. For some values of the parameters there are trajectories which go arbitrary far from the fixed points.
ISSN:2070-0466
2070-0474
DOI:10.1134/S2070046615010045