Preprint

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

Murod KhamraevDepartment of Mathematics University of Manchester Manchester UKFarrukh MukhamedovDepartment of Mechanics and Mathematics, National University of Uzbekistan, Vuzgorodok, Tashkent 700174, Uzbekistan

ArXiv.orgrepository2005en

ABI

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.

Topics

advanced mathematical theories Mathematical Dynamics and Fractals

Identifiers

DOI: 10.48550/arxiv.math/0511204

Citations and references

Cited by 03 references

Metrics — AkademScholar