Normal forms of bireversible vector fields

Autor(es)

Baptistelli, P. H. ^[1] ; Manoel, M. ^[2] ; Zeli, I. O. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Estadual Maringa, Dept Math, BR-87020900 Maringa, Parana - Brazil

^[2] Univ Sao Paulo, ICMC, Dept Math, CP 668, BR-13560970 Sao Carlos, SP - Brazil

^[3] IEF ITA, Dept Math, BR-12228900 Sao Jose Dos Campos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: BULLETIN DES SCIENCES MATHEMATIQUES; v. 154, p. 102-126, AUG 2019.
• Citações Web of Science: 0

Resumo

In this paper we adapt the method of Baptistelli, Manoel, and Zeli (2016) {[}6] to obtain normal forms of a class of smooth bireversible vector fields. These are vector fields reversible under the action of two linear involution and whose linearization has a nilpotent part and a semisimple part with purely imaginary eigenvalues. We show that these can be put formally in normal form preserving the reversing symmetries and their linearization. The approach we use is based on an algebraic structure of the set of this type of vector fields. Although this can lead to extensive calculations in some cases, it is in general a simple and algorithmic way to compute the normal forms. We present some examples, which are Hamiltonian systems without resonance for one case and other cases with certain resonances. (C) 2019 Elsevier Masson SAS. All rights reserved. (AU)

• Processo FAPESP: 12/23591-1 - Teoria de singularidades em sistemas dinâmicos descontínuos na presença de simetria
• Beneficiário: Iris de Oliveira Zeli
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado