论文标题
P-ADIC动力学的阴影和稳定性
Shadowing and Stability in p-adic dynamics
论文作者
论文摘要
在本文中，我们将动力学属性研究为$ \ Mathbb {z} _p $和$ \ Mathbb {q} _p $的阴影和结构稳定性，其中$ p \ geq 2 $是质量数字。 In particular, we prove that if $f: \mathbb{Z}_p \to \mathbb{Z}_p$ is a $(p^{-k},p^{m})$ ( $0 < m \leq k$ integers ) locally scaling map then $f$ is shadowing and structurally stable.我们还研究了这些地图的共轭类别的数量，并以$ 1 $ -lipschitz地图为$ \ mathbb {z} _p $的上述属性，以及$ \ mathbb {q} _p $的移位地图，收缩和扩张的扩展。
In this paper, we study dynamical properties as shadowing and structural stability for a class of dynamics on $\mathbb{Z}_p$ and $\mathbb{Q}_p$, where $p \geq 2$ is a prime number. In particular, we prove that if $f: \mathbb{Z}_p \to \mathbb{Z}_p$ is a $(p^{-k},p^{m})$ ( $0 < m \leq k$ integers ) locally scaling map then $f$ is shadowing and structurally stable. We also study the number of conjugacy classes of these maps and we consider the above properties for $1$-Lipschitz maps of $\mathbb{Z}_p$ and for extensions of the shift map, contractions and dilatations on $\mathbb{Q}_p$.
