Omega-limit sets for the Stein-Ulam spiral map

We consider a quadratic map of the 2-dimensional simplex to itself, studied by Stanisław Ulam and Paul Stein in the 1950's. Those maps arise in the theory of population genetics. One of them has the behavior much different than the 96 other ones. We determine the typical $\omega$-limit set for this map, answering a question of Vallander from 1972. This is a joint work with Michał Misiurewicz.