Statistical and probabilistic properties for weakly chaotic systems

The purpose of the project is to study limit laws and mixing properties for weakly chaotic systems.

The theory of strongly chaotic systems has been extensively developed in the last decades and there are now methods that can be used in studying their statistical properties: e.g. a functional analytic approach (transfer operators, anisotropic Banach spaces) or a geometric approach (distribution of stable and unstable foliations).

However much less is known for systems which do not have such a strong chaotic behavior and in particular are of zero entropy.

In the project I plan to develop general methods to study many natural classes of systems which exhibit slower (or weaker) notions of randomness (or chaos), e.g. suspension flows.

I plan to study mixing and statistical properties of such systems with the goal of characterizing their chaotic behavior and compare it with strongly chaotic systems.

In particular, I also plan to study the infinite measure case where the theory has not yet been developed and where possibly other notions of mixing have to be developed.