2019
DOI: 10.1016/j.bulsci.2019.02.002
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Normal forms of bireversible vector fields

Abstract: In this paper we adapt the method of [P. H. Baptistelli, M. Manoel and I. O. Zeli. Normal form theory for reversible equivariant vector fields. Bull. Braz. Math. Soc., New Series 47 (2016), no. 3, 935-954] 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 pres… Show more

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Cited by 2 publications
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“…where the bar denotes the closure of the set and L is the linearization of the vector field at the origin. In this case, the normal form process introduces additional symmetries into the problem since every vector field is formally conjugated to a vector field with symmetry group S. Several works deal with vector fields that present symmetric geometric configurations, as we can see in [4,5,9,15,18]. In particular, in the same way as Elphick et al [14] and based on algebraic invariant theory, Baptistelli, Manoel and Zeli present a method ([4, Theorem 4.7]) to obtain normal forms of a reversible equivariant vector field that preserve the symmetries of the original vector field.…”
Section: Introductionmentioning
confidence: 99%
“…where the bar denotes the closure of the set and L is the linearization of the vector field at the origin. In this case, the normal form process introduces additional symmetries into the problem since every vector field is formally conjugated to a vector field with symmetry group S. Several works deal with vector fields that present symmetric geometric configurations, as we can see in [4,5,9,15,18]. In particular, in the same way as Elphick et al [14] and based on algebraic invariant theory, Baptistelli, Manoel and Zeli present a method ([4, Theorem 4.7]) to obtain normal forms of a reversible equivariant vector field that preserve the symmetries of the original vector field.…”
Section: Introductionmentioning
confidence: 99%