A new construction of the unstable manifold for the measure-preserving Hénon map

Let $H$ denote the measure-preserving Hénon map with the parameter $a > 0$. The map $H$ has a hyperbolic fixed point $\boldsymbol{p}$. The main result of this paper is that the unstable mainfold of $\boldsymbol{p}$ is the iterated limit of a very simple set. Informally,

$W^u(\boldsymbol{p}) = \lim_{n\to\infty} H^n(\mathcal L)$

where $\mathcal L$ is the line $y=-x$ and $W^u(\boldsymbol{p})$ denotes the unstable manifold of $\boldsymbol{p}$.