Renato Huzak

Fractal analysis of canard cycles with two breaking parameters and applications

This work has been supported in part by Croatian Science Foundation under the project IP-2014-09-2285.

Cyclicity of degenerate graphic \begin{document}

In this paper we finish the study of the cyclicity ( i.e. the maximum number of limit cycles) of the degenerate graphic \begin{document}

DF_{2a}

DF_{2a}

\end{document} of Dumortier-Roussarie-Rousseau program

\end{document} of [ 6 ] which is initiated in [ 5 ]. More precisely, we prove that the graphic \begin{document}

Limit cycles in slow-fast codimension 3 saddle and elliptic bifurcations

DF_{2a}

Primary birth of canard cycles in slow-fast codimension 3 elliptic bifurcations

\end{document} has a finite cyclicity. The goal of the program [ 6 ] is to solve the finiteness part of Hilberts 16th problem for quadratic polynomial systems. We use techniques from geometric singular perturbation theory, including the family blow-up.