Krieger’s generator theorem shows that any free invertible ergodic measure preserving action (Y,\mu, S) can be modelled by A^Z (equipped with the shift action) provided the natural entropy constraint is satisfied; we call such systems (here it is A^Z) universal. Along with Tom Meyerovitch, we establish general specification like conditions under which Z^d-dynamical systems are universal. These conditions are general enough to prove that
1) A self-homeomorphism with almost weak specification on a compact metric space (answering a question by Quas and Soo)
Abstract: During the last 20 years there has been a considerable literature on a collection of related mathematical topics: higher degree versions of Poncelet’s Theorem, certain measures associated to some finite Blaschke products and the numerical range of finite dimensional completely non-unitary contractions with defect index 1. I will explain that without realizing it, the authors of these works were discussing OPUC.