2013/10/18 by U. A. Rozikov, Rozikov, U. A., I. A. Sattarov +1 · 1 citation
Mathematics · #11S99 #12J12 #30D05 #46S10 #54H20 #Dynamical Systems (math.DS) #FOS: Mathematics #advanced mathematical theories #math.DS #msc:11S99 #msc:12J12 #msc:30D05 #msc:46S10 #msc:54H20
paper · pdf · doi:10.48550/arxiv.1310.4942
12 pages
arxiv created 2013/10/18 · openalex publication_date 2013/10/18 · arxiv updated 2013/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the behavior of trajectories of a (3,2)-rational p-adic dynamical system in the complex p-adic filed \mathbb Cp, when there exists a unique fixed point x0. We study this p-adic dynamical system by dynamics of real radiuses of balls (with the center at the fixed point x0). We show that there exists a radius r depending on parameters of the rational function such that: when x0 is an attracting point then the trajectory of an inner point from the ball Ur(x0) goes to x0 and each sphere with a radius >r (with the center at x0) is invariant; When x0 is a repeller point then the trajectory of an inner point from a ball Ur(x0) goes forward to the sphere Sr(x0). Once the trajectory reaches the sphere, in the next step it either goes back to the interior of Ur(x0) or stays in Sr(x0) for some time and then goes back to the interior of the ball. As soon as the trajectory goes outside of Ur(x0) it will stay (for all the rest of time) in the sphere (outside of Ur(x0)) that it reached first.