33 citations · 42 across the 14 of their papers we have counts for
16 papers
Divergent diagrams of folds associated with reflections
Patrícia Hernandes Baptistelli, Maria Elenice Rodrigues Hernandes, Miriam Manoel
We analyse divergent diagrams of \(k\)-fold map-germs on \((\mathbb{C}^n,0)\), for , associated with reflections, adapting to the complex setting the theory of folds a…
A Symmetry-Based Classification of Synchrony in Tree Networks
Nicolas Brito, Miriam Manoel
Coupled cell systems model interacting dynamical units and provide a natural framework for studying synchrony phenomena arising from collective behavior. Graph symmetries often ind…
On affine homogeneous polynomial centrosymmetric matrices
Miriam Manoel, Leandro Nery
We explore a class of centrosymmetric matrices whose entries are polynomials in two variables, referred to as DNA matrices. Our motivation stems from an unexpected connection betwe…
Synchrony patterns in Laplacian networks
Tiago Amorim, Miriam Manoel
A network of coupled dynamical systems is represented by a graph whose vertices represent individual cells and whose edges represent couplings between cells. Motivated by the impac…
The realization of admissible graphs for coupled vector fields
Tiago Amorim, Miriam Manoel
In a coupled network cells can interact in several ways. There is a vast literature from the last twenty years that investigates this interacting dynamics under a graph theory form…
Equivariant mappings and invariant sets on Minkowski space
Miram Manoel, Leandro Nery de Oliveira
In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some know…
Recognition of symmetries in reversible maps
Patrícia H. Baptistelli, Isabel S. Labouriau, Miriam Manoel
We deal with germs of diffeomorphisms that are reversible under an involution. We establish that this condition implies that, in general, both the family of reversing symmetries an…
Quotients and lifts of symmetric directed graphs
Manuela Aguiar, Ana Dias, Miriam Manoel
Given a directed graph, an equivalence relation on the graph vertex set is said to be balanced if, for every two vertices in the same equivalence class, the number of directed edge…
Normal forms of bireversible vector fields
P. H. Baptistelli, M. Manoel, I. O. Zeli
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 4…
On equivariant binary differential equations
Miriam Manoel, Patrícia Tempesta
This paper introduces the study of occurrence of symmetries in binary differential equations (BDEs). These are implicit differential equations given by the zeros of a quadratic 1-f…
Gradient systems on coupled cell networks
Miriam Manoel, Mark Roberts
For networks of coupled dynamical systems we characterize admissible functions, that is, functions whose gradient is an admissible vector field. The schematic representation of a g…
Relative equivariants under compact Lie groups
Patricia Hernandes Baptistelli, Miriam Manoel
In this work we obtain the general form of polynomial mappings that commute with a linear action of a relative symmetry group. The aim is to give results for relative equivariant p…
Complete transversals of reversible equivariant singularities of vector fields
Miriam Manoel, Iris de Oliveira Zeli
We use group representation theory to give algebraic formulae to compute complete transversals of singularities of vector fields, either in the nonsymmetric or in the reversible eq…
Normal form theory for reversible equivariant vector fields
Patricia Hernandes Baptistelli, Miriam Garcia Manoel, Iris de Oliveira Zeli
We give an alternative method to obtain normal forms of reversible equivariant vector fields. We adapt the classical method using tools from invariant theory to establish formulae…
The Wigner caustic on shell and singularities of odd functions
Wojciech Domitrz, Miriam Manoel, Pedro de M. Rios
We study the Wigner caustic on shell of a Lagrangian submanifold L of affine symplectic space. We present the physical motivation for studying singularities of the Wigner caustic o…
Invariants and relative invariants under compact Lie groups
Patricia H. Baptistelli, Miriam Manoel
This paper presents algebraic methods for the study of polynomial relative invariants, when the group G formed by the symmetries and relative symmetries is a compact Lie group. We…