Appears in collections : Jean-Morlet chair: Tiling and recurrence / Chaire Jean-Morlet : Pavages et récurrence, Exposés de recherche

In this talk we explain how the Fibonacci trace map arises from the Fibonacci substitution and leads to a unified framework in which a variety of models can be studied. We discuss the associated foliations, hyperbolic sets, stable and unstable manifolds, and how the intersections of the stable manifolds with the model-dependent curve of initial conditions allow one to translate dynamical into spectral results.