Evolution equations for eigenvalues and coefficients of polynomials and related generalized dynamics

TL;DR

This paper introduces a new classification of polynomials and develops evolution equations for their roots and coefficients, leading to a generalized dynamics framework extending relativistic dynamics.

Contribution

It proposes a novel classification scheme for polynomials and derives evolution equations that preserve polynomial classes, creating a new generalized dynamics model.

Findings

Derived evolution equations for polynomial roots and coefficients.

Established a classification scheme for polynomials.

Developed a generalized dynamics framework extending relativistic dynamics.

Abstract

In this paper we suggest new classification of polynomials and evolution equations for the roots and the coefficients remaing the polynomials within proper class. In the basis of the developed evolution equations we built new dynamics generalizing the relativistic dynamics.