Por Fabio Armando Tal (Universidade de São Paulo).

We review some recent results describing the behaviour of conservative homeomorphisms of surfaces with zero topological entropy. Using mostly techniques from Brouwer theory, we show that the dynamics of such maps in the sphere is very restricted and, in many ways, similar to that of an integrable flow. We also show that many of these restrictions are still valid for 2-torus homeomorphisms.