Dynamical systems defined by polynomials with algebraic properties
Number Theory
2026-05-21 v6
Abstract
Let (x_n; n\in Z) be a bisequence of elements x_n in the 1-dimensional torus R/Z, which is called a stream over R/Z. Let P(z)=a_k z^k+...+a_1 z+a_0 be a polynomial with integer coefficients. Define the set of streams over R/Z such that the convolution product P(z)\times(x_n; n\in Z)=(\sum_{i=0}^k a_i x_{n-i}; n\in Z)=(0; n\in Z), which is called the stream 0 of P. We study similarities between stream 0 of P and the roots of P(z)=0.
Cite
@article{arxiv.2502.12888,
title = {Dynamical systems defined by polynomials with algebraic properties},
author = {Shigeki Akiyama and Xiang Gao and Teturo Kamae},
journal= {arXiv preprint arXiv:2502.12888},
year = {2026}
}