Topological atlas of the Kowalevski–Sokolov top

Topological classification of Liouville foliations for the Kovalevskaya integrable case on the Lie algebra so(3, 1)

“…1) The bifurcation diagram Σ a,0 , i.e. the image of a critical set in an orbit M 4 a,0 , can be obtained from diagrams Σ an,bn for orbits M 4 an,bn constructed in [6] by passing to the limit (a n , b n ) → (a, 0). This follows from the compactness of the following set A for fixed ε < 0 and h 0 :…”

“…In this section we will calculate all the Fomenko-Zieschang invariants for every 3-dimensional regular isoenergy submanifold Q 3 of the Kovalevskaya integrable case on so (3,1). The list of rough molecules (see [1]) was constructed in [6]. It remains to find the marks of these molecules.…”

“…The first case is the limit of the Kovalevskaya case on so(3, 1) when κ → −0. And the second one is the limit of the Kovalevskaya-Sokolov case when ε 0 −→ 0 (see [6]). Lemma 4.1.…”

“…In this paper we generalize the results of [2] to the analogue of the Kovaleskaya system on so (3,1) using the results of M. P. Kharlamov, P. E. Ryabov and A. Yu. Savushkin [6]. More precisely, we calculate all the marks of the rough molecules found in [6], thus obtaining all the Fomenko-Zieschang invariants of the system.…”

“…, γ 11 : (λ γ 11 , λ β 4 ) (7) (λ γ 11 , −λ β 3 ) (2,5) , δ 3 : (λ δ 3 , λ β 4 ) (7) , ξ 6 : (λ ξ 6 , λ γ 5 ) (6) .…”