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arXiv · 2406.16887

Generalized nonautonomous dynamics through groupoid morphisms

Néstor Jara·Emir Molina
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Abstract

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.

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Néstor Jara, Emir Molina. 2024-04-26. Generalized nonautonomous dynamics through groupoid morphisms. https://arxiv.org/abs/2406.16887

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