The so-called Hilbert–Smale problem asks for the maximum number of limit cycles that In this thesis we prove the existence of coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f" , having at least limit cycles. All these limit cycles are hyperbolic and surround a hyperbolic focus. Also these limit cycles are relaxation oscillations, in the sense that the speed close to the fast orbit is of order , while the speed near the slow curves is of order . The relaxation oscillation itself is of size . The proof is based on geometric singular perturbation theory or slow-fast systems. Finally we prove that any ltr"
