The cascades route to chaos
Thursday, November 15, 2012 - 10:30am - 12:00pm
In 1958, Pekka Myrberg was the first to discover that as a parameter c is varied in the iterated quadratic map, periodic orbits occur with the progression of periods k, 2k, 4k, 8k, ... for a large variety of k values. Subsequently, this phenomenon of period-doubling cascades has been seen in a large variety of parameter-dependent dynamical systems, be they iterated maps, ordinary differential equations, partial differential equations, delay differential equations, or even experimental observations. It has often been observed that cascades occur in a dynamical system as the system transitions from ordered to chaotic. In this talk, I will be presenting some recent results based on work of Alligood, Mallet-Paret, and Yorke to explain the link between chaos and cascades.