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This article extends the theorem of the absence of wandering domains fromunimodal maps to infinitely period-doubling renormalizable H\'enon-like maps inthe strongly dissipative (area contracting) regime. The theorem solves an openproblem proposed by several authors [van Strien (2010) and Lyubich and Martens(2011)], and covers a class of maps in the nonhyperbolic higher dimensionalsetting. The classical proof for unimodal maps breaks down in the H\'enonsettings, and two techniques, "the area argument" and "the good region and thebad region", are introduced to resolve the main difficulty. The theorem alsohelps to understand the topological structure of the heteroclinic web for suchkind of maps: the union of the stable manifolds for all periodic points isdense.

Nonexistence of Wandering Domains for Infinitely Renormalizable H\'enon Maps