Cohomological equations on dynamical systems arising from Delone sets.

Series: 
Math Physics Seminar
Thursday, April 15, 2010 - 14:05
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Facultad de Matematicas, Pontificia Universidad Catolica de Chile, Santiago, Chile
,  
Organizer: 

The speaker is visiting Georgia Tech for the full week. His office will be Skiles 133A.

This talk concerns aperiodic repetitive Delone sets and the dynamical systems associated with them. A typical example of an aperiodic repetitive Delone set is given by the set of vertices of the Penrose tiling. We show that natural questions concerning aperiodic repetitive Delone sets are reduced to the study of some cohomological equations on the associated dynamical systems. Using the formalism of tower systems introduced by Bellissard, Benedetti, and Gambaudo, we will study the problem about the existence of solution of these cohomological equations.