On products of skew rotations

الأصل · EN

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⁾=Sʰ²₂· S₁ʰ¹ under some conditions on H₁, H₂. We study in this paper asymptotical properties of trajectories of T⁽ʰ¹,ʰ²⁾.