| Résume | Two measurable bijections of a standard probability space are orbit equivalent if they have the same orbits up to conjugacy. In recent years, odometers have been an central class of systems for explicit constructions of orbit equivalences, using their combinatorial structure. In this talk we introduce a construction of orbit equivalence between odometers and new systems that we call odomutants. The starting point for this notion is a construction of Feldman in 1976, which enables to get a first flexibility result about even Kakutani equivalence. Here we deal with a second result, about entropy.
It follows from work of Kerr and Li that if the cocycles are log integrable, the entropy is preserved. Our construction of odomutants shows that their result is optimal, namely we find odomutants of positive entropy orbit equivalent to an odometer, with almost log integrable cocycles. |
