THE CALCULATION OF THE PROBABILITY DENSITY IN PHASE SPACE OF A CHAOTIC SYSTEM ON THE EXAMPLE OF ROTATOR IN THE HARMONIC FIELD

Alexander V. Liapzev

Alexander V. Liapzev Herzen State Pedagogical University of Russia, Moika river embankment, 48, 191186, Saint Petersburg, Russia

Keywords: nonlinear dynamics, chaos, chaotic attractor, the density of the probability distribution of States, semiclassical limit

Abstract

The method of calculating the probability density distribution for chaotic systems described by the equations of classical nonlinear dynamics is proposed. Specific calculations are performed for the rotator in an external harmonic field. The results of calculation of probability density distribution in the cross section of the phase space are compared with the Poincare cross section for the chaotic attractor obtained by numerical solution of the dynamic equations. It is shown that the corresponding quantum problem for a rotator in an external harmonic field in the semiclassical limit leads to equations describing the distribution of probability density in the classical case.

Author Biography

Alexander V. Liapzev, Herzen State Pedagogical University of Russia, Moika river embankment, 48, 191186, Saint Petersburg, Russia

PhD, professor of the Department of methods of teaching physics at RSPU A. I. Herzen, lav@herzen.spb.ru

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