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 $$\mathbb{C}_p$$ . 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.

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