Maximally symmetric bifurcations of Morse functions on two-dimensional surfaces (Q1584131)

In the theory of Liouville foliations of integrable systems there appears the problem of description of bifurcations of Morse functions. In [\textit{A.~T.~Fomenko}, Russ. Math. Surv. 44, No.~1, 181-219 (1989; Zbl 0694.58012)]\ a notion of atom was introduced. An atom is a neighborhood of a connected critical level of a function \(f\) which is considered with a precision up to the layer-wise framing of the equivalence. The author introduces the notion of maximal symmetric atom and proves a series of assertions on the existence of maximal symmetric atoms.