The non-smooth pitchfork bifurcation: a renormalization analysis

Luke Adamson, Andrew Harold Osbaldestin

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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 specied 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.
Original languageEnglish
Pages (from-to)224-240
JournalDynamical Systems
Volume30
Issue number2
Early online date23 Jan 2015
DOIs
Publication statusPublished - 2015

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