Vladlen Timorin

Topological models for some quadratic rational maps

We will discuss quadratic rational self-maps of the Riemann sphere.
For maps with a critical cycle of period two, and the other
critical point on the boundary of its immediate basin of attraction,
explicit topological models will be given.
This means that such maps are relatively simple,
since explicit topological models are even unknown for
some maps of the form z^2+c.
The maps we consider, together with countably many
parabolic maps, form the "external boundary" of the
bifurcation locus in the plane of quadratic rational
maps with a period 2 critical orbit.