Submission date: 18 September 2022

Abstract:

We study the definable topological dynamics (G(M), S_G(M)) of a definable group acting on its type space, where M is either an o-minimal structure or a p-adically closed field, and G a definable amenable group. We focus on the problem raised by Neweslki of whether weakly generic types coincide with almost periodic types, showing that the answer is positive when G has boundedly many global weakly generic types. We also give two "minimal counterexamples" where G has unboundedly many global weakly generic types, extending the main results of On minimal flows, definably amenable groups, and o-minimality to a more general context.

Mathematics Subject Classification: 03C98 37B05 11E95 03C64 43A07

Keywords and phrases:

Full text arXiv 2209.08495: pdf, ps.