Speaker: Wayne Hayes
Department of Computer Science
University of California, Irvine
Title: Tinkerbell is Chaotic
We introduce a new containment method for proving the existence of shadows of chaotic dynamical systems, that does not require the map to be injective. We then apply this method to the "Tinkerbell" map, which is not injective. We then use a method introduced by Stoffer and Palmer (1999) using "branching points" to demonstrate an infinite family of infinitely long orbits that can be mapped one-to-one to arbitrary, infinite-length binary strings. The existence of such a one-to-one mapping proves that the Tinkerbell map is chaotic.
This is work in collaboration with Alexandre Goldstejn of CNRS Nantes and Pieter Collins of CWI Amsterdam.