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Abstract <p> This article is dedicated to the study of dynamical systems over the field of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic numbers in higher dimension, defined by a specific monomial function in each component. We determine a condition on the Jacobian matrix for a point to be an attractor of the system. We also found basins of attraction and centers of Siegel disks in terms of basins of attraction and Siegel disks of its components, respectively. </p>

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Dynamical Systems Defined Over \(p\)-Adics in Higher Dimension

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • J. Galeano-Peñaloza,
  • O. F. Casas-Sánchez

摘要

Abstract

This article is dedicated to the study of dynamical systems over the field of \(p\) -adic numbers in higher dimension, defined by a specific monomial function in each component. We determine a condition on the Jacobian matrix for a point to be an attractor of the system. We also found basins of attraction and centers of Siegel disks in terms of basins of attraction and Siegel disks of its components, respectively.