This note presents some advances regarding the Lyapunov constants of some families of planar polynomial differential systems, as a first step toward the resolution of the center and cyclicity problems. First, a parallelization approach is computationally implemented to achieve the 14th Lyapunov constant of the complete cubic family. Second, a technique based on interpolating some specific quantities so as to reconstruct the structure of the Lyapunov constants is used to study a Kukles system, some fifth-degree homogeneous systems, and a quartic system with two invariant lines
AbstractFor real planar autonomous analytic differential equations we introduce the notion of persis...
We study the kind of centers that Hamiltonian Kolmogorov cubic polynomial differential systems can e...
Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited an...
Agraïments: The first author is supported by the NSF of China (No. 11201086, No.11401255) and the Ex...
It is well known that the number of small amplitude limit cycles that can bifurcate from the origin ...
AbstractBy using an effective complex algorithm to calculate the Lyapunov constants of polynomial sy...
By using an effective complex algorithm to calculate the Lyapunov constants of polynomial systems E,...
We prove that there are one-parameter families of planar differential equations for which the cente...
The analysis of system behaviour near boundary of the stability domain requires the computation of L...
In 1991, Chicone and Jacobs showed the equivalence between the computation of the first-order Taylor...
AbstractIn the last years many papers giving different methods to compute the Poincaré–Liapunov cons...
AbstractIn this paper we describe a mechanical procedure for computing the Liapunov functions and Li...
This dissertation is mainly a study of the center problem in the context of a family of three dimens...
"The computation of Lyapunov quantities is closely connected with the important in engineering mecha...
AbstractIn this paper generalized Poincaré-Lyapunov constants Vi, i = 1, 2,…, are defined and an exp...
AbstractFor real planar autonomous analytic differential equations we introduce the notion of persis...
We study the kind of centers that Hamiltonian Kolmogorov cubic polynomial differential systems can e...
Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited an...
Agraïments: The first author is supported by the NSF of China (No. 11201086, No.11401255) and the Ex...
It is well known that the number of small amplitude limit cycles that can bifurcate from the origin ...
AbstractBy using an effective complex algorithm to calculate the Lyapunov constants of polynomial sy...
By using an effective complex algorithm to calculate the Lyapunov constants of polynomial systems E,...
We prove that there are one-parameter families of planar differential equations for which the cente...
The analysis of system behaviour near boundary of the stability domain requires the computation of L...
In 1991, Chicone and Jacobs showed the equivalence between the computation of the first-order Taylor...
AbstractIn the last years many papers giving different methods to compute the Poincaré–Liapunov cons...
AbstractIn this paper we describe a mechanical procedure for computing the Liapunov functions and Li...
This dissertation is mainly a study of the center problem in the context of a family of three dimens...
"The computation of Lyapunov quantities is closely connected with the important in engineering mecha...
AbstractIn this paper generalized Poincaré-Lyapunov constants Vi, i = 1, 2,…, are defined and an exp...
AbstractFor real planar autonomous analytic differential equations we introduce the notion of persis...
We study the kind of centers that Hamiltonian Kolmogorov cubic polynomial differential systems can e...
Isochronicity and linearizability of two-dimensional polynomial Hamiltonian systems are revisited an...