  Let $\varphi_0$ be a smooth area-preserving diffeomorphism of a compact
surface $M$ and let $\Lambda_0$ be a horseshoe of $\varphi_0$ with Hausdorff
dimension strictly smaller than one. Given a smooth function $f:M\to
\mathbb{R}$ and a small smooth area-preserving perturtabion $\varphi$ of
$\varphi_0$, let $L_{\varphi, f}$, resp. $M_{\varphi, f}$ be the Lagrange,
resp. Markov spectrum of asymptotic highest, resp. highest values of $f$ along
the $\varphi$-orbits of points in the horseshoe $\Lambda$ obtained by
hyperbolic continuation of $\Lambda_0$.
  We show that, for generic choices of $\varphi$ and $f$, the Hausdorff
dimension of the sets $L_{\varphi, f}\cap (-\infty, t)$ vary continuously with
$t\in\mathbb{R}$ and, moreover, $M_{\varphi, f}\cap (-\infty, t)$ has the same
Hausdorff dimension of $L_{\varphi, f}\cap (-\infty, t)$ for all
$t\in\mathbb{R}$.
