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We present groupoid morphisms as an algebraic structure for nonautonomousdynamics, as well as a generalization of group morphisms, which describeclassic dynamical systems. We introduce the structure of cotranslations, as aspecific kind of groupoid morphism, and establish a correspondence betweencotranslations and skew-products. We give applications of cotranslations tononautonomous equations, both in differences and differential. We obtainresults about the differentiability of cotranslations, as well as dimensioninvariance and diagonalization (through a generalized notion of kinematicsimilarity) for a partial version of them, admitting noninvertibletransformations.

Groupoid morphisms as an algebraic structure for nonautonomous dynamics