2024/04/26 by Néstor Jara, Jara, Néstor, Emir Molina +1
Computer Science · Mathematics · #18B40 #37B55 #37C60 #37C85 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2406.16887
openalex publication_date 2024/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the notions of nonautonomous dynamics to arbitrary groups, through groupoid morphisms. This also presents a generalization of classic dynamical systems and group actions. We introduce the structure of cotranslations, as a specific kind of groupoid morphism, and establish a correspondence between cotranslations and skew-products. We give applications of cotranslations to nonautonomous equations, both in differences and differential. Our results delve into the differentiability of cotranslations, along with dimension invariance and diagonalization, utilizing a generalized notion of kinematic similarity.