On a non-linear p-adic dynamical system

نویسندگان

چکیده

We investigate the behavior of trajectories a $(3,2)$-rational $p$-adic dynamical system in complex filed ${\mathbb C}_p$, when there exists unique fixed point $x_0$. study this by dynamics real radiuses balls (with center at $x_0$). show that radius $r$ depending on parameters rational function such that: $x_0$ is an attracting then trajectory inner from ball $U_r(x_0)$ goes to and each sphere with $>r$ $x_0$) invariant; When repeller forward $S_r(x_0)$. Once reaches sphere, next step it either back interior or stays $S_r(x_0)$ for some time ball. As soon as outside will stay (for all rest time) (outside $U_r(x_0)$) reached first.

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ژورنال

عنوان ژورنال: Uzbek Mathematical Journal

سال: 2021

ISSN: ['2010-7269']

DOI: https://doi.org/10.29229/uzmj.2021-1-15