Does a closed form solution exist that can give both ${\displaystyle x_{n}}$and ${\displaystyle y_{n}}$given ${\displaystyle x_{0}}$, ${\displaystyle y_{0}}$, ${\displaystyle a}$, ${\displaystyle b}$, and ${\displaystyle n}$? --Melab±1 ☎ 23:29, 13 February 2012 (UTC)[reply]

Probably not. The closest I can find is this article [1], which gives exact solutions to a stabilized henon map (the topic is "controlling chaos"). I know you are interested in closed form solutions, but part of why these systems are studied is that it is very computationally cheap to generate orbits. If you want to know the state at n=1000,or even 10^10, these can be computed in a matter of seconds on a modern computer. SemanticMantis (talk) 15:35, 14 February 2012 (UTC)[reply]