International Organization for Standardization (ISO) defines roundness of a 2D object as the ratio of the radius of the inscribed circle, to the radius of the circumscribed circle. In our work we are interested in ISO roundness of rotation sets of a parametric family of dynamical systems on the surface of the torus. We also introduce an alternative definition of roundness for this family of sets, find its upper and lower bounds, non-monotonicity and discover points of discontinuity. 

The rotation sets are topological invariants that describe all asymptotic behaviours of all the orbits, in terms of direction and magnitude. 
This is joint work with B. Perrot (Paris-Sacley) and A. Clark (Queen Mary University London).