All literature that I read about Hénon maps state that they are the 'product of a 2D manifold by a Cantor set.' Now, I know what a 2D manifold, a Cantor set is and a cartesian product is. But I am not able to visualize the product of the 2D manifold and a Cantor set.
$ℝ^1× ℝ^1$ is a plane. So the product of a 1D space with itself is a 2D space. What then is the dimension of the product a 2D space by a Cantor set (non-integer dimension) and is this the same as the dimension of the Hénon map for when $a = 1.4$ and $b = 0.3$? Am I even right to extend the observation that the dimension of $ℝ^1 × ℝ^1$ is 2?