Duck trajectories of relaxation systems connected with violation of the normal switching conditions

Assume that for $x\in R$ and $y\in R^2$ at an isolated point of discontinuity of the relaxation system
$$ \varepsilon\dot x=f(x,y),\quad\dot y=g(x,y),\qquad0<\varepsilon\ll1, $$
the so-called normal switching condition is violated generically. Under this assumption a theorem on the existence and the asymptotic properties of two structurally stable duck trajectories is proved. Their role in the dynamics of relaxation systems is stressed.
Bibliography: 6 titles.