Let H1​(p,q), H2​(p,q) be two time-independent Hamiltonians with one
degree of freedom and {S1t​}, {S2t​} be the one-parametric groups of
shifts along the orbits of Hamiltonian systems generated by H1​, H2​. In
some problems of population genetics there appear the transformations of the
plane having the form T(h1​,h2​)=S2h2​​⋅S1h1​​ under some
conditions on H1​, H2​. We study in this paper asymptotical properties of
trajectories of T(h1​,h2​).Comment: 13 pages, 10 figure