Qualitative changes in sound intensities frequently occur in musical signals and Hopf
bifurcation control is the most natural mathematical approach to study them. We propose a …

For perturbations of integrable non-Hamiltonian quasi-homogeneous planar vector field
whose origin is a non-degenerate singular point, orbital linearization and analytic …

In this work we use the normal form theory to establish an algorithm to determine if a planar
vector field is orbitally reversible. In previous works only algorithms to determine the …

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 …

We are concerned with the simplest normal forms of non-resonant double Hopf oscillators
with radial nonlinearities. Due to the required Lie algebraic structure for preserving the radial …

Analytical Integrability of Perturbations of Quadratic Systems | Mediterranean Journal of
Mathematics Skip to main content SpringerLink Account Menu Find a journal Publish with us …

In this work is characterized the analytic integrability problem around a nilpotent singularity
for differential systems in the plane under generic conditions. The analytic integrability …

We present a wide class of differential systems in any dimension that are either integrable or
complete integrable. In particular, our result enlarges a known family of planar integrable …

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We consider a class of three-dimensional systems having an equilibrium point at the origin,
whose principal part is of the form (−∂ h∂ y (x, y),∂ h∂ x (x, y), f (x, y)) T. This principal …