On Hopf cyclicity of planar systems with multiple parameters (Q2484659)

The authors deal with a planar system of the form \[ \dot x= H_y+\varepsilon p(x,y,\varepsilon,\delta),\quad \dot y= -H_x+\varepsilon q(x,y,\varepsilon,\delta),\tag{1} \] where \(\varepsilon\) is a small parameter, \(\delta\in D\subset\mathbb{R}^n\) with \(D\) bounded, \(n\geq 1\), and \(H\), \(p\), \(q\) are given \(C^\infty\) functions. The main purpose of this paper is the problem of cyclicity for the Hopf bifurcation of (1) with several parameters.