On Rational $P$-Adic Dyanamical Systems

Details On Rational $P$-Adic Dyanamical Systems On Rational $P$-Adic Dyanamical Systems

2005-11-08

arxiv.org/abs/math/0511205v2

Published in Methods of Funct. Anal. Topology 10(2004), 21-31

Mathematics

Dynamical Systems

15 pages

Scientific paper

In the paper we investigate the behavior of trajectory of rational $p$-adic dynamical system in complex $p$-adic filed $\C_p$. It is studied Siegel disks and attractors of such dynamical systems. We show that Siegel disks may either coincide or disjoin for different fixed points of the dynamical system. Besides, we find the basin of the attractor of the system. It is proved that such kind of dynamical system is not ergodic on a unit sphere with respect to the Haar measure.

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