Boundary-of-chaos conjecture for Hénon maps

Let $\mathcal H$ be the Hénon family $F_{a,b}(x,y)=(x^2+a-by,x)$ with $a,b\in\mathbb R$, and let $\partial_{\operatorname{chaos}}$ denote the boundary in $\mathcal H$ of the set of maps with zero entropy. Boundary-of-chaos conjecture. The set $\partial_{\operatorname{chaos}}$ is a piece-wise real analytic curve consisting of infinitely renormalizable Hénon maps. The claim describes the expected geometric organization of the transition between zero-entropy and chaotic dynamics in the Hénon family; the supplied text gives no resolution.