EVENT DETAILS AND ABSTRACT

Title: Tower systems for linearly repetitive systems
Speaker: Jose Aliste-Prieto
Speaker Info: CMM, University of Chile
Brief Description:
Special Note:
Abstract:

Quasicrystals are solids that do not exhibit periodicity yet they show some long range order (in the form of Bragg peaks in the X-ray diffraction). Non-periodic linearly repetitive Delone sets have been proposed as models for them by Lagarias and Pleasants. One successful way of studying such sets is by using dynamical systems theory. In fact, the associated dynamical system has a structure of generalized-solenoid. In this talk, we introduce tower systems for these solenoids, which are a generalization of the classical construction of Kakutani Rohlin partitions. We then follow the work of Benedetti, Bellissard and Gambaudo, and show how to construct tower systems for linearly repetitive systems with good properties, the main one being a uniform bound on the norm of the transition matrices. Finally, we briefly discuss applications of this construction. This is joint work with D. Coronel.