It is a notoriously difficult task to determine the exact periods of periodic orbits of a given chaotic system in the plane. This is due to the fact that in dimension 2, in general, there is no forcing theory analogous to Sharkovskii's Theorem in dimension 1. Although density of homoclinic intersections guarantees density of periodic points, and existence of infinitely many periods, this does not guarantee any specific periods. In this collaboration with Dyi-Shing Ou and Przemek Kucharski from AGH Kraków, we rigorously determine an open region in the parameter space for which Lozi maps exhibit periodic points of least period n, for all n> 13. Lozi maps are piecewise affine transformations of the plane given for a fixed parameter (a,b) (typically in [-2,2]x[-1,1]), by L(x,y)=(-a|x|-by+(a-b-1),x).