FIKUSZ

Penrose tilings and dynamical systems in view of noncommutative geometry

First some simple examples are shown from the theory of aperiodic tilings and dynamical systems, which both lead to similar, but very "strange" mathematical structures -- although these two fields are very different at first sight.

These structures are ill-behaved factor spaces, which cannot be handled with the tools of ordinary topology. Then via these examples we demonstrate the power of the new tools, offered by noncommutative geometry, for the study of these structures.