Qualitative Theory of Planar Differential Systems

By Freddy Dumortier, Joan Carles Artés Ferragud, Jaume Llibre. 2006

986 citations recorded by the source corpus.

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In Geometry and Topology

Citations in the corpus

Uniqueness of limit cycles for Liénard differential equations of degree four (2012, neutral): “23 of [2] for instance.”
Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields (2014, background): “For details about these theorems, see Chapters 1 and 6 of [10].”
On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry (2013, background): “21 in [5], we can define two new functions P̂R and P̂L such that for each Y = PZ(y) + y > 0 we take P̂Z(Y ) = PZ(y) − y, where y > 0 and Z ∈ {L,R}.”
Bi-center problem and bifurcation of limit cycles from nilpotent singular points in Z2-equivariant cubic vector fields (2018, methodology): “With the help of Maple, phase portraits of some cases were given in [13].”
Spectral sequences and parametric normal forms (2011, background): “Some related results can be found in [12,19,33].”
Piecewise linear perturbations of a linear center (2013, background): “It is well known that a smooth linear system with an isolated monodromic singular point has not singular points at infinity, that is the infinity is a periodic orbit in the Poincaré compactification, see [7].”
A Survey on the Inverse Integrating Factor (2009, background): “The definition of parabolic or elliptic sector can be found, for instance, in [44].”
On the Darboux Integrability of Polynomial Differential Systems (2012, methodology): “The proof of the classification of all centers of planar polynomial differential systems of degree 2 can be strongly simplified using the Darboux first integrals, see Schlomiuk [38] and the chapter 8 of Dumortier, Llibre and Artés [16].”