Now showing items 1-16 of 16

• #### Analytic integrability inside a family of degenerate centers ﻿

(Elsevier, 2016)
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 imply formal orbital equivalence to a ...
• #### Analytic integrability of some examples of degenerate planar vector fields ﻿

(Springer, 2016)
This paper is devoted to the classification of analytic integrable cases of two families of degenerate planar vector fields with a monodromic singular point at the origin. This study falls in the still open degenerate ...
• #### 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 ...
• #### Center conditions for nilpotent cubic systems using Cherkas method ﻿

(Elsevier, 2016)
In this work we study the center problem of a cubic polynomial differential system with nilpotent linear part. The analysis is based on the application of the Cherkas method to the Takens normal form. The study needs many ...
• #### Center problem for systems with two monomial nonlinearities ﻿

(American Institute of Mathematical Sciences, 2016)
We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. ...
• #### Center problem in the center manifold for quadratic differential systems in R^3 ﻿

(Elsevier, 2016)
Using tools of computer algebra based on the Gröbner basis theory we derive conditions for the existence of a center on a local center manifold for fifteen seven-parameter families of quadratic systems on R 3. To obtain ...
• #### Centers and isochronous centers for generalized quintic systems ﻿

(Elsevier, 2015)
In this paper we classify the centers and the isochronous centers of certain polynomial differential systems in R2 of degree d≥5 odd that in complex notation are ż=(λ+i)z(zz̄)d−52(Az5+Bz4z̄+Cz3z̄2+Dz2z̄3+Ezz̄4+Fz̄5), ...
• #### Centers for generalized quintic polynomial differential systems ﻿

(Rocky Mountain Mathematics Consortium, 2017)
• #### Integrability conditions of a resonant saddle in Liénard-like complex systems ﻿

(Elsevier, 2016)
We consider a complex differential system with a resonant saddle that remind the classical Liénard systems in the real plane. For such systems we determine the conditions of analytic integrability of the resonant saddle.
• #### 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 Lotka-Volterra planar complex cubic systems ﻿

(World Scientific, 2016)
In this paper we study the Lotka-Volterra 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, ...
• #### Reversible nilpotent centers with cubic homogeneous nonlinearities ﻿

(Elsevier, 2016)
We provide 13 non--topological equivalent classes of global phase portraits in the Poincaré disk of reversible cubic homogeneous systems with a nilpotent center at origin, which complete the classification of the phase ...
• #### The three-dimensional center problem for the zero-Hopf singularity ﻿

(American Institute of Mathematical Sciences, 2016-03-01)
In this work we extend well-known techniques for solving the Poincar\'e-Lyapunov nondegenerate analytic center problem in the plane to the 3-dimensional center problem at the zero-Hopf singularity. Thus we characterize the ...