\'Etude des op\'erateurs d'\'evolution en caract\'eristique 2

TL;DR

This paper investigates the classification of evolution operators in characteristic 2 algebras, focusing on nilpotent, quasi-constant, periodic, and plenary train types across baric and non-baric cases.

Contribution

It provides a comprehensive classification of evolution operators in characteristic 2 algebras, including nonassociative and baric structures, which was previously unexplored.

Findings

Classification of four types of evolution operators in characteristic 2

Distinction between baric and non-baric algebra cases

Identification of properties for nilpotent, quasi-constant, periodic, and plenary train operators

Abstract

We are interested in the evolution operators defined on commutative and nonassociative algebras when the scalar field is of characteristic 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic and plenary train operators. They are studied and classified for non baric and for baric algebras.