Fast-Slow partially hyperbolic systems

Fast-slow systems appear naturally in many physical systems, especially in presence of locally conserved quantities. I am particularly interested in the case in which the fast variables undergo a chaotic motions. Unfortunately, while averaging and homogenization theory provide some information about the moderately long time behaviour, very little is know about the asymptotical statistical properties of such systems. To start developing a general theory for this type of systems, I will discuss the simplest possible model and illustrate which kind of results can currently be obtained. (Joint work with Roberto Castorrini).