ABSTRACT
Let us comment on the “Sturmian property” of the basic (L-S) family of similarity profiles {fl(y)}{l≥0}. Figures 2.12 and 2.15 indicate that, regardless the oscillatory exponential tails, each profile fl(y) has a clear “approximate” (“nonlinear”) Sturmian structure and exhibits l+1 dominant extrema (meaning l “transversal” zeros in between). In a rigorous mathematical sense, such properties are known to hold for the second-order problems. In the first sections, where (2) was studied, Sturmian properties were con-
nected with the category of the functional subset for each fl, being the corresponding min-max critical point of the functional, since the category assumes
FIGURE 2.13
FIGURE 2.14
and
FIGURE 2.15
FIGURE 2.16
using the reflection of the functions (·) → −(·). Hence, the nodal sets of fl(y) get more and more complicated as l increases (there is still no rigorous treatment of such zero-set phenomena).
