Fractal analysis of planar nilpotent singularities and numerical applications

The goal of our work is to give a complete fractal classification of planar analytic nilpotent singularities. For the classification, we use the notion of box dimension of (two-dimensional) orbits on separatrices generated by the unit time map. We also show how the box dimension of the one-dimensional orbit generated by the Poincaré map, defined on the characteristic curve near the nilpotent center/focus, reveals an upper bound for the number of limit cycles near the singularity. We introduce simple formulas for numerical calculation of the box dimension of one-and two-dimensional orbits and apply them to nilpotent singularities.

Publication year:2021

Keywords:Keyword: nilpotent singularity, box dimension, unit-time map, Poincaré map

BOF-keylabel:yes

IOF-keylabel:yes

BOF-publication weight:6

Authors:International

Authors from:Higher Education

Accessibility:Open