A note on the box dimension of degenerate foci

2017/04/30 by Vlah, Domagoj, Zubrinic, Darko, Zupanovic, Vesna
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.00372

Abstract

We study polynomial planar systems with singularity of focus type without characteristic directions. Simple and natural transformation of weak focus has been used to obtain such degenerate focus. We compute the box dimension of a spiral trajectory, and show connection to cyclicity of the system under a perturbation.

Related

• The box dimension of degenerate spiral trajectories of a class of\n ordinary differential equations
• Fractal Analysis of Pseudo Foci in Piecewise Analytic Systems
• Focus-focus singularities in classical mechanics
• Center-focus determination and limit cycles bifurcation for p:q homogeneous weight singular point
• A note on focus-focus singularities