Hénon map
= Hénon map
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The Hénon map is a two-parameter quadratic planar map, conventionally $(X,Y)\mapsto(1-aX^2+Y,b_HX)$. The alternative family $(x,y)\mapsto(y,\mu-bx-y^2)$ has constant Jacobian determinant $b$. When $\mu\ne0$, the change $X=y/\mu$, $Y=-bx/\mu$ gives the conventional parameters $a=\mu$, $b_H=-b$. Fixed points in the alternative normalization satisfy $x=y$ and $y^2+(1+b)y-\mu=0$. Its invertibility requires $b\ne0$; at $b=1$ it preserves area.