On products of skew rotations

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 trans...

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Bibliographic Details
Published inarXiv.org
Main Authors Arnold, M D, Dinaburg, E I, Dobrushina, G B, Pirogov, S A, Rybko, A N
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.12.2011
Subjects
Hamiltonian functions
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Summary: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 \(T^{(h_1,h_2)}\).
ISSN:2331-8422