Geometry, Topology and Dynamics Seminar
Jose Aliste Prieto
University of Chile, Santiago
On a generalization of Poincare classification theorem for aperiodic actions
Abstract: The description of quasiperiodic structures has a long tradition in mathematical physics, in particular since the discovery of quasicrystals in the early 80's. Frequently, the modelling of such structures leads to different types of dynamical systems which include, depending on the concept of quasiperiodicity that is used, skew products over quasiperiodic or almost-periodic base flows, mathematical quasicrystals or maps of the real line with almost-periodic displacement.
A first problem that arises is to know whether there is a uniqueness of rotation/translation number. First, we will recall known results. Next, an important problem in this context is to know whether the considered system is semiconjugate to a rigid translation. We solve this problem in a general setting that includes all the above-mentioned examples, thus providing a Poincare-like existence result. Most of the content of this talk is joint work with T. Jager from TU Dresden.
Monday May 2, 2011 at 3:00 PM in SEO 636