Project Goals

Our main goal in this project is to study the dynamical properties of Lie Group actions on closed manifolds and foliations which present some interesting dynamical property.  We introduced the concept of expansive Lie group actions, and studied some of  their aspects.

We are mainly focused on the following problems:

1- What are the chaotic properties of expansive Lie group actions?
2-  What are the main properties of expansive foliations?
3- If a foliation is dynamically generated by some diffeomorphism or group action, what are the implications of such foliation to the generating dynamics?
4-  Which partially hyperbolic diffeomorphisms do generate expansive foliations? 
5- Which manifolds support expansive foliations?