Morse theory plays a key role in modern mathematics. The main idea of this theory is the study of manifolds by using properties of smooth functions on them. The main construction of the theory is the construction of the cellular decomposition of the manifold in accordance with a given smooth function on it and the location of singular points of these functions. Purely, this construction requires that all critical points have pairwise different critical values. In the last few years, in some problems of Hamiltonian mechanics, a particular interest in functions on 2-manifolds with several singular points on the same singular level arose. The corresponding mathematical notion is called an atom. It was introduced by Fomenko in [3].
展开▼
