Complete transversals of symmetric vector fields

Miriam Manoel and Iris de Oliveira Zeli

Journal of Singularities
volume 12 (2015), 124-130

Received 14 March 2014. Received in revised form 18 September 2014.

DOI: 10.5427/jsing.2015.12h

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Abstract:

We use group representation theory to obtain complete transversals of singularities of vector fields in nonsymmetric as well as reversible and equivariant contexts. The method is an algebraic alternative to compute complete transversals, producing normal forms to be applied systematically in the local analysis of symmetric dynamics.


Keywords:

Normal forms, equivariance, reversibility, complete transversal


Mathematical Subject Classification:

37C80, 34C20, 13A50


Author(s) information:

Miriam Manoel, corresponding author Iris de Oliveira Zeli
University of São Paulo University of Campinas
Mathematics Department IMECC - Mathematics Department
P.O. Box 668 P. O. Box 6065
13560-970, São Carlos - SP, Brazil 13083-859, Campinas - SP, Brazil
email: miriam@icmc.usp.br email: irisfalkoliv@ime.unicamp.br