Browsing Articles publicats (Matemàtica) by Subject "Integrability"
Now showing items 113 of 13

A survey of isochronous centers
(Edicions de la Universitat de Lleida, 1999) 
A survey on the inverse integrating factor
(Springer, 2010)The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles ... 
Averaging methods of arbitrary order, periodic solutions and integrability
(Elsevier, 2016)In this paper we provide an arbitrary order averaging theory for higher dimensional periodic analytic differential systems. This result extends and improves results on averaging theory of periodic analytic differential ... 
Centers for the Kukles homogeneous systems with odd degree
(London Mathematical Society, 2015)For the polynomial differential system x˙ = −y, y˙ = x+Qn(x; y), where Qn(x; y) is a homogeneous polynomial of degree n there are the following two conjectures done in 1999. (1) Is it true that the previous system for ... 
Formal inverse integrating factors and the nilpotent center problem
(World Scientific Publishing, 2016)We are interested in deepening knowledge of methods based on formal power series applied to the nilpotent center problem of planar local analytic monodromic vector fields X. As formal integrability is not enough to ... 
Integrability Conditions for Complex Homogeneous Kukles Systems
(Atlantis and Taylor & Francis, 2018)In this paper we study the existence of local analytic first integrals for complex polynomial differential systems of the form ẋ = x + Pn(x, y), ẏ = −y, where Pn(x,y) is a homogeneous polynomial of degree n, called the ... 
Integrability conditions for complex kukles systems
(Taylor & Francis, 2017)In this paper, we provide necessary and sufficient conditions for the existence of local analytic first integrals for a seventhparameter family of complex cubic systems called the complex Kukles systems. 
Integrability conditions for Lotka–Volterra planar complex quintic systems
(Elsevier, 2010)In this paper we obtain necessary and sufficient integrability conditions at the origin for the Lotka–Volterra complex quintic systems which are linear systems perturbed by fifth degree homogeneous polynomials, i.e., we ... 
Integrability conditions of a resonant saddle perturbed with homogeneous quintic nonlinearities
(Springer, 2015)In this work we complete the integrability conditions (i.e. conditions for the existence of a local analytic first integral) for a family of a resonant saddle perturbed with homogeneous quintic nonlinearities studied in a ... 
Integrability of complex planar systems with homogeneous nonlinearities
(Elsevier, 2016)In this paper we obtain sufficient conditions for the existence of a local analytic first integral for a family of quintic systems having homogeneous nonlinearities. The family studied in this work is the largest one ... 
Integrability of LotkaVolterra planar complex cubic systems
(World Scientific, 2016)In this paper we study the LotkaVolterra complex cubic systems. We obtain necessary conditions of integrability for these systems with some restriction on the parameters. The sufficiency is proved for all conditions, ... 
Linearizability of planar polynomial Hamiltonian systems
(Elsevier, 2022)Isochronicity and linearizability of twodimensional polynomial Hamiltonian systems are revisited and new results are presented. We give a new computational procedure to obtain the necessary and sufficient conditions for ... 
The role of algebraic solutions in planar polynomial differential systems
(Cambridge University Press, 2007)We study a planar polynomial differential system, given by . We consider a function , where gi(x) are algebraic functions of with ak(x) and algebraic functions, A0(x,y) and A1(x,y) do not share any common factor, h2(x) is ...