  Let $H_1(p,q)$, $H_2(p,q)$ be two time-independent Hamiltonians with one
degree of freedom and $\{S_1^t\}$, $\{S_2^t\}$ be the one-parametric groups of
shifts along the orbits of Hamiltonian systems generated by $H_1$, $H_2$. In
some problems of population genetics there appear the transformations of the
plane having the form $T^{(h_1,h_2)}=S^{h_2}_2\cdot S_1^{h_1}$ under some
conditions on $H_1$, $H_2$. We study in this paper asymptotical properties of
trajectories of $T^{(h_1,h_2)}$.

Dynamical Systems