The Falkner-Skan equation. I: The creation of strange invariant sets
The paper contains a detailed study of bifurcations in the Falkner-Skan equation \[ y'''+ y'' y+ \lambda(1- (y')^2)= 0\tag{1} \] for values \(\lambda> 0\). The authors show the machinery of these bifurcations which lead to the birth of complicated invariant sets of (1) and occur as \(\lambda\) increases through positive integer values. In particular, an almost complete account of the creation of the most interesting admissible solutions (for those \(\sup_{x\in R} |y'(x)|< \infty)\) by bifurcations from two trajectories \(y'= \pm 1\) is given. Although the equation (1) has the symmetry properties (it is reversible by Sevryuk), the authors do not make essential use of this symmetry in their investigation. One may state that a new codimension one bifurcation phenomenon in general parametrized families of differential equations is discovered in this paper. It is worth pointing out that the most part of this well written work is self-contained.
scientific article; zbMATH DE number 784944