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Data on sampling long-term monthly mean distributions of Antarctic sea ice extent are analyzed for the period of 1974-2013. In the framework of propositions on the nature of variations in the components of limited-area system, the numerical model of sea ice extent dynamics was developed. It is demonstrated that in 1974-2013 the variations in monthly mean sea ice extent were defined by semiannual, annual, 30-year, and 60-year periodic components. The interpolation of the obtained results is presented. The forecast of Antarctic sea ice conditions for 2015-2135 is given. [ABSTRACT FROM AUTHOR]