In this paper we consider perturbations of quasi-homogeneous planar Hamiltonian systems,
where the Hamiltonian function does not contain multiple factors. It is important to note that …

We characterize the nilpotent systems whose lowest degree quasi-homogeneous term is (y,
σxn) T, σ=±1, having a formal inverse integrating factor. We prove that, for n even, the …

This paper uses tools in quasi-homogeneous normal form theory to discuss certain aspects
of reversible vector fields around an equilibrium point. Our main result provides an …

In this work, we analyze some aspects of the center problem from the perspective of the
normal form theory. We provide alternative proofs of some well known results in the case of …

We give necessary conditions for the orbital-reversibility for a class of planar dynamical
systems, based on properties of some invariant curves. From these necessary conditions we …

In this paper we study the analytic integrability around the origin inside a family of
degenerate centers or perturbations of them. For this family analytic integrability does not …

In this paper, we explore the normal form of fully inhomogeneous feed forward network
dynamical systems, characterized by a nilpotent linear component. We introduce a new …

This paper presents a study of a three-parameter unfolding of a degenerate case in the Hopf-
-saddle-node singularity. This analysis shows that this nonlinear degeneracy is a source of …

In this paper we use the orbital normal form of the nondegenerate Hopf-zero singularity to
obtain necessary conditions for the existence of first integrals for such singularity. Also, we …

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