  The purpose of this article is to study the relation between combinatorial
equivalence and topological conjugacy, specifically how a certain type of
combinatorial equivalence implies topological conjugacy. We introduce the
concept of kneading sequences for a setting that is more general than
one-dimensional dynamics: for the two-dimensional toy model family of H\'enon
maps introduced by Benedicks and Carleson, we define kneading sequences for
their critical lines, and prove that these sequences are a complete invariant
for a natural conjugacy class among the toy model family. We also establish a
version of Singer's Theorem for the toy model family.

Dynamical Systems