Complete Transversal and Formal Normal Forms of Vector Fields

Ramírez-Carrasco S.; Fernández-Sánchez P. · Boletim da Sociedade Paranaense de Matematica (2023) · DOI: 10.5269/bspm.46354

Resumen

Inspired by the complete transversal technique we establish a classification of vector fields by normal forms. In the case of vector fields with non zero linear part in (C2 , 0) and nilpotent vector fields in (C3, 0), we recover the classical normal forms for these vector fields, and we provide a different formal normal form from that presented by Takens in dimension 2. We also get the formal normal form for vector fields in (C, 0) with a fixed multiplicity. © Soc.

Instituciones: Universidad Nacional Mayor de San Marcos; Pontificia Universidad Católica del Perú