On Some of the Differences Between Z and Z^2 in Dynamics
- Date: 01/11/2007
Klaus Schmidt (University of Vienna)
University of Washington
Around 1970 it was discovered that measure preserving actions of Z^2 on
probability spaces can have remarkably different properties from
Z-actions, i.e. from actions of single transformations. Many of these
differences can be described as 'rigidity phenomena' and manifest
themselves in the scarcity of certain objects for Z^2-actions which are
abundant for Z-actions: they may have unexpectedly few invariant
probability measures, invariant sets, isomorphisms or automorphisms.
This lecture will aim to explain--in some examples--both the reasons and the ramifications of these rigidity phenomena.
10th Anniversary Speaker Series 2007