| Project Detail |
In chaos theory, understanding weakly chaotic systems poses a formidable challenge. While strides have been made in analysing strongly chaotic systems, those with zero entropy remain elusive. Supported by the Marie Sklodowska-Curie Actions (MSCA) programme, the ErgodicHyperbolic project will study the statistical properties and limit laws governing such systems. Using both functional analytic and geometric approaches, researchers seek to unravel the mysteries of slower, weaker chaos exhibited by various natural classes of systems, including suspension flows. The ultimate goal? To characterise their chaotic behaviour, compare it with strongly chaotic systems, and pioneer new notions of mixing, especially in the unexplored realm of infinite measures.
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. |
