The topology of isoenergy surfaces for the Sokolov integrable case on the Lie algebra so(3, 1)

Abstract

Sokolov’s integrable case on so(3, 1) is studied. This is a Hamiltonian system with two degrees of freedom where both the Hamiltonian and additional integral are homogeneous polynomials of degrees 2 and 4, respectively. The topology of isoenergy surfaces is described for different values of parameters.