arXiv subjects

Patrícia Hernandes Baptistelli

Publications and source records attributed to Patrícia Hernandes Baptistelli.

3 recordsLinked to original sources

arXiv2026

Divergent diagrams of folds associated with reflections

We analyse divergent diagrams of $k$-fold map-germs on $(\mathbb{C}^n,0)$, for $k, n \geq 2$, associated with reflections, adapting to the complex setting the theory of folds associated with involutions on $(\mathbb{R}^n,0)$. In the complex case, a $k$-fold is naturally related to a cyclic group generated by a reflection, which guides the analytic classification of singularities. Under the conditions of transversality and linearity of the associated reflections, certain conditions related to the nontrivial eigenvalues appear as invariants by simultaneous conjugacy. We also provide a complete classification of pairs of transversal linear reflections and the corresponding divergent diagrams.

math.CV↗

arXiv2022

Normal forms of $ω$-Hamiltonian vector fields with symmetries

In this paper, we present algebraic tools to obtain normal forms of $ω$-Hamiltonian vector fields under a semisymplectic action of a Lie group, by taking into account the symmetries and reversing symmetries of the vector field. The normal forms resulting from the process preserve the Hamiltonian condition and the types of symmetries of the original vector field. Our techniques combine the classical method of normal forms of Hamiltonian vector fields with the invariant theory of groups.

math.DS↗

arXiv2022

$ω$-Symplectic algebra and Hamiltonian vector fields

The purpose of this paper is presenting a theoretical basis for the study of $ω$-Hamiltonian vector fields in a more general approach than the classical one. We introduce the concepts of $ω$-symplectic group and $ω$-semisymplectic group, and describe some of their properties. We show that the Lie algebra of such groups is a useful tool in the recognition of an $ω$-Hamiltonian vector field defined on a symplectic vector space $(V,ω)$ with respect to coordinates that are not necessarily symplectic.

math.SG↗