Time change rigidity for unipotent flows
报告人：Daren Wei (National University of Singapore)
时间：2023-07-14 15:10-17:00
地点：Room 1418, Science Building No.1
Abstract: Two flows are said to be Kakutani equivalent if one is isomorphic to the other after time change, or equivalently if there are Poincare sections for the flows so that the respective induced maps are isomorphic to each other. Ratner showed that if G=SL(2,R) and \Gamma is a lattice in G, and if U is a one parameter unipotent subgroup in G then the U action on G equipped with Haar measure is loosely Bernoulli, i.e. Kakutani equivalent to a circle rotation. Thus any two such systems SL(2,R)/\Gamma are Kakutani equivalent to each other. On the other hand, Ratner showed that if G'=SL(2,R) x SL(2,R) and \Gamma' is a reducible lattice, and U' is the diagonally embedded one parameter unipotent subgroup in G', then (G'/\Gamma', U', m) is not loosely Bernoulli. We show that in fact in this case and many other situations one cannot have Kakutani equivalence between such systems unless they are actually isomorphic. This is a joint work with Elon Lindenstrauss.
