A continuous equivariant map from the Floyd boundary of a finitely generated
relatively hyperbolic group (RHG for short) to its Bowditch boundary is
constructed. Such a map is unique unless the group is two-ended. We consider a
RHG as a group acting on a compactum discontinuously on triples and cocompactly
on pairs. We describe and make use a rather general construction of "attractor
sum" of two actions of a locally compact group.