Attractors of Piecewise Smooth Maps

I will review some of the methods and results available to describe attractors of piecewise smooth maps. The structure of non-wandering sets, the existence of invariant measures, and the dimension of bifurcating attractors will be addressed with varying levels of generality. I believe that the methods available to prove these results are just as important as the results themselves, and these techniques (and hopes for extensions of these techniques) will be the main driver of the talk.