2023/03/11 by Konstantin Mischaikow, Mischaikow, Konstantin, Charles A. Weibel +1 · 1 citation
Chemistry · Mathematics · #68Q25 #68R10 #68U05 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Molecular spectroscopy and chirality
paper · pdf · doi:10.48550/arxiv.2303.06492
openalex publication_date 2023/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns the computation and identification of the (homological) Conley index over the integers, in the context of discrete dynamical systems generated by continuous maps. We discuss the significance with respect to nonlinear dynamics of using integer, as opposed to field, coefficients. We translate the problem into the language of commutative ring theory. More precisely, we relate shift equivalence in the category of finitely generated abelian groups to the classification of ℤ[t]-modules whose underlying abelian group is given. We provide tools to handle the classification problem, but also highlight the associated computational challenges.