Abstract
We investigate behavior of trajectory of a (3, 2)-rational p-adic dynamical system in complex p-adic field \(\mathbb{C}_p\). 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: P-Adic Numbers, Ultrametric Analysis, and Applications
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.