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Fundamental problem of high latitude magnetosphere is the problem of mapping of observed at low altitudes structures to the equatorial plane. Developed during the latest period models of the Earth’s magnetic field partially solved this problem. However, statistical character of these models, great level of turbulent fluctuations in the geomagnetic tail even during quite periods and inner magnetosphere during disturbed periods greatly complicate the process of mapping. Another problem is the inapplicability the approximation of the ideal MHD in the conditions of magnetostatic equilibrium and slow plasma motion. It is impossible, for example, to analyze magnetic flux transport in the magnetosphere without simultaneous analysis of the changes of external boundary conditions formed in the process of the solar wind interaction with the geomagnetic field.One of the main changes in the analysis of magnetospheric dynamics is the use of plasma pressure as the parameter conserved along magnetic field line in the condition of magnetostatic equilibrium for mapping of low altitude auroral structures to the equatorial plane. We analyze the main changes of the description of magnetospheric dynamics appeared taking into account such mapping results. The formation of magnetic holes and humps in the ring current and tail regions and their role in the magnetospheric dynamics are discussed