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Splitting equivariant dynamics

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Il Nuovo Cimento B (1971-1996)

Summary

We prove that any dynamical system on aG manifoldM which is equivariant under theG action, can be decomposed into, the semi-direct product of an autonomous dynamics in theG orbit space Ω=M/G, and a dynamics (depending on theG orbit) onG. This result is actually a corollary of Michel theorem (L. Michel,C. R. Acad. Sci. Paris A,272 (1971) 433) on the geometry of symmetry breaking, and uses the same ingredients for the proof. It permits to unify a number of known and useful results in the literature, as discussed here.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University of Technology, LE11 3TU, Loughborough, UK

    G. Gaeta

  2. Centre de Physique Théorique, Ecole Polytechnique, 91128, Palaiseau, France

    G. Gaeta

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  1. G. Gaeta
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Correspondence to G. Gaeta.

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Work supported in part by the Italian CNR under grant no. 203.01.62

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Gaeta, G. Splitting equivariant dynamics. Nuov Cim B 110, 1213–1226 (1995). https://doi.org/10.1007/BF02724611

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