First we provide new properties about the vanishing multiplicity of the inverse integrating factor of a planar analytic differential system at a focus. After we use this vanishing multiplicity for studying the cyclicity of foci with pure imaginary eigenvalues and with homogeneous nonlinearities of arbitrary degree having either its radial or angular speed independent of the angle variable in polar coordinates. After we study the cyclicity of a class of nilpotent foci in their analytic normal form. © 2013 Elsevier Inc.
|Journal||Journal of Differential Equations|
|Publication status||Published - 1 Dec 2013|
- Cyclicity of a focus
- Inverse integrating factor
- Limit cycles
- Vanishing multiplicity