  We introduce and study tame homeomorphisms of surfaces of infinite type.
These are maps for which curves under iterations do not accumulate onto
geodesic laminations with non-proper leaves, but rather just a union of
possibly intersecting curves or proper lines. Assuming an additional finiteness
condition on the accumulation set, we prove a Nielsen-Thurston type
classification theorem. We prove that for such maps there is a canonical
decomposition of the surface into invariant subsurfaces on which the first
return is either periodic or a translation.

Geometric Topology