  We derive a sufficient condition for topological horseshoe and uniform
hyperbolicity of a 4-dimensional symplectic map, which is introduced by
coupling the two 2-dimensional H\'enon maps via linear terms. The coupled
H\'enon map thus constructed can be viewed as a simple map modeling the
horseshoe in higher dimensions. We show that there are two different types of
horseshoes, each of which is realized around different anti-integrable limits
in the parameter regime.
