Time and entry-exit relation near a planar turning point (Q1886971)

The authors consider the problem of transition of orbits near the turning points in models with very general setting, where canard solutions are known to exist. They study the transition time problem as well as the entry--exit relation at such turning points by using a geometric approach. The manifolds of canard solutions are in general only \(C^0\) at this points that makes a classical asymptotic approach impossible. The applied method involves a family of blow up transformations of the turning point and the use of \(C^k\)-normal forms and center manifolds.