Period-doubling cascades galore

By E. Sander, James A. Yorke. Ergodic Theory and Dynamical Systems, 2009

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Abstract The appearance of numerous period-doubling cascades is among the most prominent features of parametrized maps, that is, smooth one-parameter families of maps F: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 generic F.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6638da419060ba2ce1cd05e1621a0e1f02d0197c