The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
By Héctor Giacomini, Jaume Giné Mesa, Jaume Llibre. 2005
113 citations recorded by the source corpus.
Abstract In this work we study the centers of planar analytic vector fields which are limit of linear type centers. It is proved that all the nilpotent centers are limit of linear type centers and consequently the Poincare–Liapunov method to find linear type centers can be also used to find the nilpotent centers. Moreover, we show that the degenerate centers which are limit of linear type centers are also detectable with the Poincare–Liapunov method.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9beebfcec83d4fc67a6349764c10cbebbd912662
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In Algebra and Number Theory
In Geometry and Topology
In Statistical and Nonlinear Physics
Citations in the corpus
- Bi-center problem and bifurcation of limit cycles from nilpotent singular points in Z2-equivariant cubic vector fields (2018, methodology): “For example, it was proved in [15] that all the nilpotent centers are limit of linear type centers and consequently the PoincaréLiapunov method to study linear type centers can be also used to consider nilpotent centers.”
- Analytic normalization of analytic integrable systems and the embedding flows (2008, background): “[2,3,6] characterize their local analytic integrability with the aid of normal forms.”
- Hamiltonian nilpotent centers of linear plus cubic homogeneous polynomial vector fields (2014, unknown): “[12], and Cima and Llibre [7].”
- A Survey on the Inverse Integrating Factor (2009, background): “The main results of [62] are summarized as follows.”