I am trying to construct a suspension that will model the Henon map.
So far I have the suspension $\dot\phi=lnA\phi$ which is a linear suspension of a mapping A. The solution to this is $\phi=e^{tlnA}\phi_0$. This holds that $\phi(1)=A\phi_0$ and $\phi(0)=\phi_0$. where A is the matrix $\begin{bmatrix} 0&1\\-j&0\end{bmatrix}$.
The problem is that this is a suspension of a linear mapping.
My next goal is to construct a suspension of a non linear mapping so that I can later create an explicit suspension for the Henon Map. I am unsure of how to go about the next step. Once again the goal is to construct a general suspension for a non linear system (like above), then apply the proper parameters to replicate the Henon Map. The Henon map is of course $\begin{bmatrix} x'\\y'\end{bmatrix}=\begin{bmatrix} 1-ax^2+y\\bx\end{bmatrix}$
Any guidance or references to creating this suspension or getting a starting point is appreciated.
Thanks