Complex integrability and linearizability of cubic Z2-equivariant systems with two 1: q resonant singular points
F Li, Y Liu, P Yu, J Wang - Journal of Differential Equations, 2021 - Elsevier
In this paper, complex integrability and linearizability of cubic Z 2-equivariant systems with
two 1: q resonant singular points are investigated, and the necessary and sufficient …
two 1: q resonant singular points are investigated, and the necessary and sufficient …
Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis
T Chen, F Li, P Yu - Journal of Differential Equations, 2024 - Elsevier
The aim of this paper is to investigate two important problems related to nilpotent center
conditions and bifurcation of limit cycles in switching polynomial systems. Due to the …
conditions and bifurcation of limit cycles in switching polynomial systems. Due to the …
[HTML][HTML] Center conditions to find certain degenerate centers with characteristic directions
We consider the two-dimensional autonomous systems of differential equations where the
origin is a monodromic degenerate singular point, ie, with null linear part. In this work we …
origin is a monodromic degenerate singular point, ie, with null linear part. In this work we …
Centers: their integrability and relations with the divergence
J Llibre - Applied Mathematics and Nonlinear Sciences, 2016 - sciendo.com
This is a brief survey on the centers of the analytic differential systems in R2. First we
consider the kind of integrability of the different types of centers, and after we analyze the …
consider the kind of integrability of the different types of centers, and after we analyze the …
Nilpotent center in a continuous piecewise quadratic polynomial Hamiltonian vector field
T Chen, J Llibre - International Journal of Bifurcation and Chaos, 2022 - World Scientific
In this paper, we study the global dynamics of continuous piecewise quadratic Hamiltonian
systems separated by the straight line x= 0, where these kinds of systems have a nilpotent …
systems separated by the straight line x= 0, where these kinds of systems have a nilpotent …
[HTML][HTML] The center problem for Z2-symmetric nilpotent vector fields
We say that a polynomial differential system x˙= P (x, y), y˙= Q (x, y) having the origin as a
singular point is Z 2-symmetric if P (− x,− y)=− P (x, y) and Q (− x,− y)=− Q (x, y). It is known …
singular point is Z 2-symmetric if P (− x,− y)=− P (x, y) and Q (− x,− y)=− Q (x, y). It is known …
Orbital reversibility of planar vector fields
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 …
vector field is orbitally reversible. In previous works only algorithms to determine the …
Nilpotent bi-center in continuous piecewise -equivariant cubic polynomial Hamiltonian systems
T Chen, S Li, J Llibre - Nonlinear Dynamics, 2022 - Springer
One of the classical and difficult problems in the theory of planar differential systems is to
classify their centers. Here we classify the global phase portraits in the Poincaré disk of the …
classify their centers. Here we classify the global phase portraits in the Poincaré disk of the …
Nilpotent centres via inverse integrating factors
In this paper, we are interested in the nilpotent centre problem of planar analytic
monodromic vector fields. It is known that the formal integrability is not enough to …
monodromic vector fields. It is known that the formal integrability is not enough to …
Formal inverse integrating factor and the nilpotent center problem
IA García - International Journal of Bifurcation and Chaos, 2016 - World Scientific
We are interested in deepening the knowledge of methods based on formal power series
applied to the nilpotent center problem of planar local analytic monodromic vector fields 𝒳 …
applied to the nilpotent center problem of planar local analytic monodromic vector fields 𝒳 …