The non-smooth pitchfork bifurcation: a renormalization analysis

Abstract

We give a renormalization group analysis of a system exhibiting a non-smooth pitchfork bifurcation to a strange non-chaotic attractor. For parameter choices satisfying two specified conditions, self-similar behaviour of the attractor on and near the bifurcation curve can be observed, which corresponds to a periodic orbit of an underlying renormalization operator. We examine the scaling properties for various parameter choices including the so-called pitchfork critical point. Finally, we study the autocorrelation function for the system and show that it is equivalent to that present in symmetric barrier billiards.

Keywords:

• strange non-chaotic attractor
• renormalization
• non-smooth pitchfork bifurcation