Period-doubling cascades galore

Abstract

AbstractThe appearance of numerous period-doubling cascades is among the most prominent features ofparametrized maps, that is, smooth one-parameter families of mapsF:ℝ×𝔐→𝔐, where 𝔐 is a smooth locally compact manifold without boundary, typically ℝN. Each cascade has infinitely many period-doubling bifurcations, and it is typical to observe that, whenever there are any cascades, there are infinitely many cascades. We develop a general theory of cascades for genericF.