Canard-cycle conjecture for simple unconnected slow curves

Let a slow-fast system on the two-torus have a slow curve $M$ with two connected components $M_1$ and $M_2$, whose projections onto the $y$-axis are disjoint arcs. Suppose each component has two jump points and both components are nondegenerate; call such an $M$ simple unconnected. For $l\in\mathbb{N}$, consider the space of slow-fast systems on the two-torus and intervals $R_n\subset\{\varepsilon>0\}$.

Canard-cycle conjecture. For every desired number $l\in\mathbb{N}$ there exists a local topologically generic set of systems such that the slow curve is nondegenerate and simple unconnected, and such that for every system in this set there is a sequence of intervals $\{R_n\}_{n=0}^{\infty}$ accumulating at zero with the property that, for every $\varepsilon\in R_n$, there exist at least $l$ canard limit cycles making one pass along the slow direction.

This conjecture extends the results for connected slow curves to simple unconnected ones. Its proposed proof requires the coexistence of two grand canards for the same value of $\varepsilon$; whether this coexistence is generic is addressed by a separate conjecture in the paper.