Recent Submissions

• Integrability of Liénard systems with a weak saddle ﻿

(Springer International Publishing, 2017)
We characterize the local analytic integrability of weak saddles for complex Li´enard systems, x˙ = y−F(x), y˙ = ax, 0 = a ∈ C, with F analytic at 0 and F(0) = F (0) = 0. We prove that they are locally integrable at the ...
• A privacy-preserving reputation system with user rewards ﻿

(Elsevier, 2017)
Reputation systems are useful to assess the trustworthiness of potential transaction partners, but also a potential threat to privacy since rating profiles reveal users’ preferences. Anonymous reputation systems resolve this ...
• Clan information market games ﻿

(Springer US, 2016)
We introduce a TU-game that describes a market where information is distributed among several agents and all these pieces of information are necessary to produce a good. This situation will be called clan information market. ...
• 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 ...
• The center problem for a 2:-3 resonant cubic Lotka–Volterra system ﻿

(Elsevier, 2013)
In this paper we obtain conditions on the coefficients of a cubic Lotka–Volterra system of the form equation(1) x=x(2-a20x2-a11xy-a02y2), ẏ=y(-3+b20x2+b11xy+b02y2), which fulfillment yields the existence in a ...
• Sex-related differences in body condition and serum biochemical parameters in red deer (Cervus elaphus) naturally infected with Mycobacterium bovis ﻿

(Elsevier, 2013)
Although Mycobacterium bovis infection is commonly reported in red deer (Cervus elaphus), potential differences in the effects of infection on male and female animals in terms of body condition and clinical biochemistry ...
• 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 ...
• Cyclicity of a class of polynomial nilpotent center singularities ﻿

(American Institute of Mathematical Sciences, 2016-04-01)
• 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 ...
• A sufficient condition in order that the real Jacobian conjecture in R^2 holds ﻿

(Elsevier, 2016)
Let F=(f,g):R2→R2 be a polynomial map such that det⁡DF(x,y) is different from zero for all (x,y)∈R2 and F(0,0)=(0,0). We prove that for the injectivity of F it is sufficient to assume that the higher homogeneous terms of ...
• Zero-Hopf polynomial centers of third-order differential equations ﻿

(Springer Science+Business Media New York, 2016-11-15)
We study the 3-dimensional center problem at the zero-Hopf singularity in some families of polynomial vector fields arising from third-order polynomial differential equations. After proving some general properties we check ...