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September 16, 2025Open Access

Floquet-like theory and gauge transformations for general smooth dynamical systems

GGGiuseppe GaetaUniversity of Milan SWSebastian WalcherUniversity of Lethbridge

Key Points

The study extends classical Floquet theory to non-autonomous, non-periodic equations, enhancing our understanding of dynamical systems.
Key examples illustrate the application of gauge transformations in transforming linear differential equations effectively.
Adopting geometric perspectives allows significant advancements in treating complex dynamical systems overall, broadening existing applications.
Gauge transformations, while well-known in physics, offer fresh insights into the mathematical treatment of dynamical systems.

Abstract

The classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of non-autonomous non-periodic equations. This is obtained by considering a change of variables which depends on time in a non-trivial way, i.e. introducing gauge transformations, well known in fundamental Physics and Field Theory -- but which seems to have received little attention in this context. V2: minor misprints corrected, examples added V3: published version

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Cite This Study

Gaeta et al. (Mon,) studied this question.

synapsesocial.com/papers/68d4508931b076d99fa584de https://doi.org/https://doi.org/10.46298/ocnmp.16278

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