  The classical Tait-Kneser theorem states that the osculating circles of a
smooth plane curve, free from curvature extrema, are pairwise disjoint. We
prove a number of analogs of this theorem, e.g., for ovals of osculating
cubics, osculating polynomials and trigonometric polynomials; in each case, we
will obtain a non-differentiable foliation with smooth leaves.
