Let $H: \mathbb{C}^2 \to \mathbb{C}^2$ be the Hénon mapping given by $$ \begin{bmatrix}x\\y\end{bmatrix} \mapsto \begin{bmatrix}p(x) - ay\\x\end{bmatrix}. $$ The key invariant subsets are $K_\pm$, the sets of points with bounded forward images, $J_\pm = \partial K_\pm$ their boundaries, $J = J_+ \cap J_-$, and $K = K_+ \cap K_-$. In this paper we identify the topological structure of these sets when $p$ is hyperbolic and $|a|$ is sufficiently small, \ie, when $H$ is a small perturbation of the polynomial $p$. The description involves projective and inductive limits of objects defined in terms of $p$ alone.