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This paper deals with the notion of integrability of flows or vector fields on two-dimensional
manifolds. We consider the following two key points about first integrals:(1) They must be …

In this paper, we investigate the linearizability problem for the two-dimensional planar
complex system. The necessary and sufficient conditions for the linearizability of this system …

In this work, we study necessary and sufficient conditions for the existence of isochronous
centers into a family of cubic time-reversible systems. This class of reversible systems is …

We study cubic polynomial differential systems having an isochronous center and an inverse
integrating factor formed by two different parallel invariant straight lines. Such systems are …

We study the maximum number of limit cycles that bifurcate from the periodic solutions of the
family of isochronous cubic polynomial centers ̇ x= y (-1+ 2 α x+ 2 β x^ 2),\quad ̇ y= x+ α …

This paper is concerned with the limit cycle problem of a cubic reversible Hamiltonian
system under perturbation of polynomials of degree n with a switching line x= 0⁠. The upper …

Our purpose in this paper is to study when a planar differential system polynomial in one
variable linearizes in the sense that it has an inverse integrating factor which can be …

In this paper we propose a constructive procedure to get the change of variables that
linearizes a smooth planar vector field on C2 around an elementary singular point (ie, a …