= Conservative Hénon stability boundary
{title2=$\det DF=1\quad(b=1)$}
At $b=1$ the <Hénon map> has unit Jacobian determinant. The upper fixed point is linearly elliptic for $-1<\mu<3$, and its newborn two-cycle is elliptic for $3<\mu<4$. These are neutral multiplier statements, not attraction. The endpoints have double multipliers $+1$ and $-1$. Constant-area scaling also excludes a simple invariant closed curve enclosing positive area when $b>0$ and $b\ne1$: invariance of its interior would require both $\operatorname{area}(F(D))=b\operatorname{area}(D)$ and $F(D)=D$. Thus the $b=1$ elliptic stability boundary is a conservative degeneracy, not a generic dissipative Neimark-Sacker bifurcation. Arbitrary non-area-preserving perturbations can change this behavior even though generic fold and flip curves persist.
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