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arXiv · 2306.17655

Groupoid morphisms as an algebraic structure for nonautonomous dynamics

Néstor Jara
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Abstract

We present groupoid morphisms as an algebraic structure for nonautonomous dynamics, as well as a generalization of group morphisms, which describe classic dynamical systems. 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. We obtain results about the differentiability of cotranslations, as well as dimension invariance and diagonalization (through a generalized notion of kinematic similarity) for a partial version of them, admitting noninvertible transformations.

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Néstor Jara. 2023-06-30. Groupoid morphisms as an algebraic structure for nonautonomous dynamics. https://arxiv.org/abs/2306.17655

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