Now showing items 1-20 of 22

• #### A counterexample to the composition condition conjecture for polynomial Abel differential equations ﻿

(Cambridge University Press, 2019)
Polynomial Abel differential equations are considered a model problem for the classical Poincaré center–focus problem for planar polynomial systems of ordinary differential equations. In the last few decades, several works ...
• #### Analytic integrability around a nilpotent singularity: The non-generic case ﻿

(American Institute of Mathematical Sciences, 2020)
Recently, in [9] is characterized the analytic integrability problem around a nilpotent singularity for differential systems in the plane under generic conditions. In this work we solve the remaining case completing the ...
• #### Analytic integrability around the origin of certain differential system ﻿

(Wilmington Scientific Publisher, 2022)
In this work we consider the polynomial differential system x˙=−y+xyn−1, y˙=x+ayxn−1, where a∈R and n≥2 with n∈N. This system is a certain generalization of the classical Liénard system. We study the center problem and ...
• #### Analytic reducibility of nondegenerate centers: Cherkas systems ﻿

(Bolyai Institute, University of Szeged; Hungarian Academy of Sciences, 2016)
In this paper we study the center problem for polynomial differential systems and we prove that any center of an analytic differential system is analytically reducible. x˙=y,y˙=P0(x)+P1(x)y+P2(x)y2, We also study the ...
• #### Center conditions and limits cycles for bilienard systems ﻿

(Texas State University, 2017)
In this article we study the center problem for polynomial BiLiénard systems of degree n. Computing the focal values and using Gröbner bases we end the center conditions for such systems for n = 6. We also establish ...
• #### Center conditions for generalized polynomial Kukles systems ﻿

(American Institute of Mathematical Sciences, 2017)
• #### Orbital Reversibility of Planar Vector Fields ﻿

(MDPI, 2021)
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 reversibility and conjugate reversibility ...
• #### The center problem and composition condition for Abel differential equations ﻿

(Elsevier, 2015)
The classical Poincaré center-focus problem for planar polynomial systems of ordinary differential equations can be transformed, in certain particular cases, to the center problem of a trigonometric Abel differential ...