2012/02/13 by U. A. Rozikov, Rozikov, U. A., Sh. N. Murodov +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1202.2690
openalex publication_date 2012/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently by Casas, Ladra and Rozikov a notion of a chain of evolution algebras is introduced. This chain is a dynamical system the state of which at each given time is an evolution algebra. The sequence of matrices of the structural constants for this chain of evolution algebras satisfies the Chapman-Kolmogorov equation. In this paper we construct 25 distinct examples of chains of two-dimensional evolution algebras. For all of these 25 chains we study the behavior of the baric property, the behavior of the set of absolute nilpotent elements and dynamics of the set of idempotent elements depending on the time.