Constructions in elliptic dynamics: recent results and open problems.
Abstract. We will discuss some recent results in the area of elliptic dynamical systems. This subject has considerable overlap with Diophantine approximation in number theory.
We will give some recent results for time changes of linear flows. The study of such time changes were originally proposed by Kolmogorov and form a prototype for KAM theory. We shall state some recent results and pose some open problems.
We will also discuss some recent results using conjugation by approximation methods and pose a number of open problems.
In both of these areas there is a dichotomy between the rigid phenomena associated with the Diophantine case and the plethora of examples obtained in the Liouville case.