Duck factory on the two-torus: multiple canard cycles without geometric constraints

Slow-fast systems on the two-torus are studied. As it was shown before, canard cycles are generic in such systems, which is in drastic contrast with the planar case. It is known that if the rotation number of the Poincare map is integer and the slow curve is connected, the number of canard limit cycles is bounded from above by the number of fold points of the slow curve. In the present paper it is proved that there are no such geometric constraints for non-integer rotation numbers: it is possible to construct generic system with as simple as possible slow curve and arbitrary many limit cycles.