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

Open Communications in Nonlinear Mathematical Physics, vol. Volume 5

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

Authors 2

1. Giuseppe Gaeta

   University of Milan

   Affiliation as printed

   Dipartimento di Matematica , Università degli Studi di Milano , v. Saldini 50 , I-20133 Milano ( Italy ) and

2. Sebastian Walcher Aachen Fachguppe Mathematik

   RWTH Aachen University · Istituto Nazionale di Fisica Nucleare, Sezione di Milano

   Affiliation as printed

   Fachguppe Mathematik , RWTH Aachen , D-52056 Aachen ( Germany)

   INFN , Sezione di Milano 2 SMRI , I-00058 Santa Marinella ( Italy)