Fully chaotic conservative models for some torus homeomorphisms - Alejo García (2024)

We study homotopic-to-the-identity torus homeomorphisms, whose rotation set has nonempty interior. We prove that any such map is monotonically semiconjugate to a homeomorphism that preserves the Lebesgue measure, and that has the same rotation set. Furthermore, the dynamics of the quotient map has several interesting chaotic traits: for instance, it is topologically mixing, it has a dense set of periodic points and it is continuum-wise expansive. In particular, this shows that a convex compact set of R^2 with nonempty interior is the rotation set of the lift of a homeomorphism of T^2 if and only if it is the rotation set of the lift of a conservative homeomorphism.