Mathematics – Dynamical Systems
Scientific paper
2011-06-29
Mathematics
Dynamical Systems
13 pages, 10 figures
Scientific paper
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 $T^{(h_1,h_2)}$.
Arnold Matthew D.
Dinaburg E. I.
Dobrushina G. B.
Pirogov Sergey A.
Rybko A. N.
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