Nonlinearity picks Aston-Bristow paper for highlight of 2013

apdc1The paper “Alternating Period Doubling Cascades” by Philip Aston and his PhD student Neil Bristow has been included in the Highlights of 2013 of the journal Nonlinearity. The paper studies cascades of period-doubling bifurcations that alternate in direction in two-dimensional maps.  By tracking the eigenvalues of a typical map throughout such cascades it is shown that there are only two qualitatively different alternating period-doubling cascades.  Renormalisation theory is applied to one class of alternating period-doubling cascades and universal spatial scalings are derived from fixed points of the appropriate renormalization operator. Universal parameter scalings are also derived from the eigenvalues of the linearization of the renormalization operator. The paper can be found here.