Classification of Reversible-Equivariant Vector Fields in 4D with Applications to Normal Forms and First Integrals

This paper uses tools in group theory and symbolic computing to give a classification of the representations of finite groups with order lower than 9 that can be derived from the study of local reversible-equivariant vector fields in $\rn{4}$. Based on such approach we exhibit, for each element in this class of dynamical systems, a simplified Belitiskii normal form and establish conditions for the existence of first integrals.