  This article extends the theorem of the absence of wandering domains from
unimodal maps to infinitely period-doubling renormalizable H\'enon-like maps in
the strongly dissipative (area contracting) regime. The theorem solves an open
problem proposed by several authors [van Strien (2010) and Lyubich and Martens
(2011)], and covers a class of maps in the nonhyperbolic higher dimensional
setting. The classical proof for unimodal maps breaks down in the H\'enon
settings, and two techniques, "the area argument" and "the good region and the
bad region", are introduced to resolve the main difficulty. The theorem also
helps to understand the topological structure of the heteroclinic web for such
kind of maps: the union of the stable manifolds for all periodic points is
dense.
