Fractal Analysis of Pseudo Foci in Piecewise Analytic Systems

Abstract

It is well known that the Minkowski dimension of spiral trajectories near a non-degenerate focus in analytic (smooth) systems is in one-to-one correspondence with the cyclicity of the focus in generic unfoldings. We give a complete fractal treatment, in terms of the Minkowski dimension and (non-)degeneracy, of spiral trajectories near pseudo foci of piecewise analytic systems. We hope these results will prove useful in the study of bifurcations of such pseudo foci through inherent geometry of associated spiral orbits.