On a nonlinear p-adic dynamical system
On a nonlinear p-adic dynamical system
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非线性 p-adic 动力系统
DOI：
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发表时间：
2013
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通讯作者：
I. A. Sattarov
中科院分区：
文献类型：
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作者：
U. Rozikov;I. A. Sattarov
研究了复p-adic域中的（3，2）-有理p-adic动力系统在存在唯一不动点x 0时的轨线行为.我们通过球的真实的半径（中心在不动点x 0）的动力学来研究这个p-adic动力系统。我们证明了存在一个半径r依赖于有理函数的参数，使得：当x 0是吸引点时，从球Ur（x 0）到内点的轨迹到x 0，并且每个半径> r的球（中心在x 0）是不变的;当x 0是排斥点时，则来自球Ur（x 0）的内部点的轨迹向前到球体Sr（x 0）。一旦轨迹到达球体，在下一步中，它要么回到Ur（x 0）的内部，要么在Sr（x 0）中停留一段时间，然后回到球的内部。一旦轨迹离开Ur（x 0），它将停留在它首先到达的球体（在Ur（x 0）之外）。
We investigate the behavior of trajectories of a (3, 2)-rational p-adic dynamical system in the complex p-adic field 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.