Péter Nándori

Title: Flexibility of ergodic properties and the central limit theorem in smooth systems

Abstract: Many smooth deterministic systems are known to satisfy the central limit theorem. Almost all of the known examples have the strongest possible chaotic property studied in ergodic theory: the Bernoulli property. We find several new examples of smooth systems satisfying the central limit theorem with only partial chaotic properties. These include (1) zero entropy, (2) weak mixing but not strong mixing, (3) mixing but not Kolmogorov, (4) Kolmogorov but not Bernoulli. We also give an example of a system satisfying the central limit theorem where the normalizing sequence is regularly varying with index 1. We will discuss the basic construction used in all of the above examples, which is a class of generalized T,T^-1 transformations. The talk is based on joint work with D. Dolgopyat, C. Dong and A. Kanigowski.