Gambaudo–Tresser renormalization conjecture for Hénon maps

Let $f_{a_*} \in \mathcal Q$ be an infinitely renormalizable quadratic polynomial with bounded type combinatorics. For $a,b \in \mathbb R$, let $F_{a,b}(x,y)=(x^2+a-by,x)$ be a Hénon map, and write $\mathcal H$ for the Hénon family. Gambaudo–Tresser renormalization conjecture. There exists a real analytic curve $\gamma(b)=(a(b),b)$ for $b\in[0,1)$ extending from $\gamma(0)=(a_*,0)$ such that $F_{\gamma(b)}\in\mathcal H$ is infinitely renormalizable and converges to the same universal renormalization limit as $f_{a_*}$ under renormalization. This is a proposed two-dimensional extension of universality for the quadratic family; the supplied text presents it as a major conjecture for Hénon-map renormalization, with no resolution stated.