Fractal analysis of planar nilpotent singularities and numerical applications

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