1991 – Behaviour of the magnetic field in the astrophysical jets is considered. Conditions when the whole jet is magnetized are provided
1992 – Conditions of the magnetic field stability in the galactic disk are obtained.
1992-1995 - The correlation function of the secular variation geomagnetic field at the Earth's surface is calculated. This function was used to solve the inverse problem on reconstruction of the correlation function at the surface of the liquid core.
1995 – The drift of the large-scale magnetic structures of the secular variation field over the past 150 years is presented. It is shown, that besides of the west drift there is a polar drift. This phenomenon was used to define the sign of the dynamo number in the core.
1997 – It is shown, that the geomagnetic polarity time scale over phanerozoic and Neogey epochs is a bi-fractal.
1997 – Basing on observations and mean field dynamo basics the qualitative estimates of the alpha-effect and dynamo-number are obtained.
1999-2001 – The 3D geodynamo model in Boussinesq approximation for the liquid Earth's core is developed.
2002-2005 – The multiprocessor large-scale and turbulent dynamo models are developed.
2003-2008 – The rapidly rotating MHD turbulence properties are considered (which include spectra, direction of the energy transfer over the spectrum), kinetic helicity generation in dynamo. The shell MHD models are constructed. This approach helped to estimate the turbulent viscosity in the liquid core of the Earth.
2009-2010 – Retardation in the feedback of the magnetic field on the helicity in Parker's dynamo model for the oscillatory magnetic field. The appearance of the parametric resonance is considered. Retardation is also responsible for long-term variations of the mean field with a period ten times longer than the original period of oscillation. These results are interesting for the galactic and solar dynamo.
2011-2013 - Numerical model of the geodynamo in the anelastic approximation was developed. The effects of compressibility in the liquid core of the Earth on the generation of helicity are investigated. The Domino model is developed, describing the behavior of the geomagnetic field in the form of a set of dipoles rotating in space.
2014-2018 - A series of works devoted to the models of the mean field in the geodynamo. Inverse problems in geodynamo. Assimilation of the data.
2019-2021 - Thermal evolution of the Earth including the nucleation of a solid core, and its connection with the geomagnetic field generation.