In this paper we study the locus of generalized degree $d$ Henon maps in the parameter space $\operatorname{ Rat}_d^N$ of degree $d$ rational maps $\mathbb{ P}^N\to\mathbb{ P}^N$ modulo the conjugation action of $\operatorname{ SL}_{ N+1}$. We show that Henon maps are in the GIT unstable locus if $N\ge3$ or $d\ge3$, and that they are semistable, but not stable, in the remaining case of $N=d=2$. We also give a general classification of all unstable maps in $\operatorname{ Rat}_2^2$.
Categories: math.DS math.AG math.NT