  We study homeomorphisms of the two-torus, homotopic to the identity, whose
rotation set has non-empty interior. For such maps, we give a purely
topological characterisation of elliptic islands in a chaotic sea in terms of
local rotation subsets. We further show that the chaotic regime defined in this
way cannot contain any Lyapunov stable points. In order to demonstrate our
results, we introduce a parameter family inspired by an example of Misiurewicz
and Ziemian.
