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Mixing for some classes of special flows over rotations of the circle. (English. Russian original) Zbl 0797.58045
Funct. Anal. Appl. 26, No. 3, 155-169 (1992); translation from Funkts. Anal. Prilozh. 26, No. 3, 1-21 (1992).
In Arnol’d’s paper [V. I. Arnol’d, Funct. Anal. Appl. 25, No. 2, 81–90 (1991); translation from Funkts. Anal. Prilozh. 25, No. 2, 1–12 (1991; Zbl 0732.58001)] it was shown that in general position the phase space of a Hamiltonian system with a multiple-valued Hamiltonian function on the two-dimensional torus can be decomposed into a finite number of cells filled by periodic trajectories and one ergodic component; over this component the phase flow is isomorphic to a special flow over rotation of the circle defined by a function with a finite number of asymmetrical logarithmic singularities. In this connection, the question of mixing for such flows arises. Our purpose is to give a positive answer to this question.

MSC:
37A25 Ergodicity, mixing, rates of mixing
70G10 Generalized coordinates; event, impulse-energy, configuration, state, or phase space for problems in mechanics
37C10 Dynamics induced by flows and semiflows
70H05 Hamilton’s equations
Citations:
Zbl 0732.58001
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References:
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