Dynamical systems with many symmetries and mild chaos: local and global classification

This project is in the area of dynamical systems and ergodic theory, more precisely the object of study are smooth dynamical systems with some chaotic behavior.

The proposed research is about persistent chaos: these are systems with mild chaotic behavior but with additional feature that they have a rich symmetry group.

The main aim is to show that persistent chaos is rigid: dynamics of such systems is essentially the same as that of algebraic maps on homogeneous spaces.

The latter systems are well understood; most common examples of such systems are geodesic and frame flows on negatively curved spaces.

The main goals are to show rigidity of persistent chaos locally, for small perturbations of mildly chaotic systems, or globally, assuming sufficiently rich symmetry group.

This proposal plans to push forward the investigation of the phenomenon of centraliser rigidity which we recently discovered: dynamics of perturbations of mildly chaotic maps with large symmetry groups may be completely classified according to the algebraic properties of the symmetry group.

The research will be carried out at KTH, where a doctoral student will be hired to work on one part of the proposed research; some parts of the project are continuation of long term collaboration with teams of researchers from Sweden, France, China and USA.

Proposed research is expected to have impact on other fields in natural sciences where chaotic systems with many symmetries are observed and play an important role.