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On a Class of Rational $P$-Adic Dynamical Systems

Murod Khamraev·Farrukh Mukhamedov
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Abstract

In this paper we investigate the behavior of trajectories of one class of rational $p$-adic dynamical systems in complex $p$-adic field $\C_p$. We studied Siegel disks and attractors of such dynamical systems. We found the basin of the attractor of the system. It is proved that such dynamical systems are not ergodic on a unit sphere with respect to the Haar measure.

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Murod Khamraev, Farrukh Mukhamedov. 2006-02-25. On a Class of Rational $P$-Adic Dynamical Systems. https://arxiv.org/abs/math/0511204

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