Fig. 12

The stretch-and-fold action of a kick followed by relaxation in the presence of shear. Left: a non-constant kick moves data away from the limit cycle (horizontal grey line). As the image of the cycle under the kick relaxes back to the cycle (under the unperturbed flow) the action of shear causes folds to appear. Right: the geometry of folding in relation to the isochron foliation (black lines). An initial segment \(\gamma_{0}\) is kicked to the blue curve and is then allowed to relax back to cycle, passing through the red and green curves, which are images of the blue curve under the unperturbed flow