The dissertation is devoted to an investigation of toroidal (ring) structures in astrophysical objects with the main original results which are the following:
1. It is shown, on the basis of an exact integral expression for the potential of a homogeneous circular torus, which is valid at any arbitrary point of space, that the outer potential of a torus can be represented with high accuracy by the potential of an infinitely thin ring of the same mass up to the torus surface. Approximate expressions for the torus potential in its outer and inner regions are obtained. It is shown that the inner potential of the torus can be represented by the potential of a cylinder and the term containing the Gaussian curvature of the torus surface (''potential of curvature'').
2. A dynamical model of obscuring tori in AGNs is simulated within the framework of the N-body problem taking into account the gravitational interaction between the clouds. It is shown that a self-gravitating thick torus in the field of the central mass remains stable, and the equilibrium cross-section has an oval shape with Gaussian density distribution, which satisfies observations.
3. It is shown that in a gravitational field of a central mass and a gravitating ring, closed circular orbits exist only to a certain radius corresponding to the last stable circular orbit, which we call ''the outermost stable circular orbit'' (OSCO) by analogy with the ISCO in the relativistic case. There is also a region of unstable equilibrium - the ''Lagrangian circle''. The existence of region with non-circular orbits between the Lagrangian circle and OSCO can explain the observed gap in the distribution of stellar density in ring galaxies. It is shown that in such a system there are closed orbits of new types in the meridian plane of the ring.
4. An essential role of the central mass in the stability of systems containing the gravitating torus is shown. Possible trajectories in the inner potential of the torus in the presence of a central mass were investigated which showed that there are at least two types of orbits in the co-moving system: halo and box orbits. It is shown that the quasi-closed halo-orbit exists in such a system. It is shown that within the framework of the problem of unperturbed motions, it is possible to form a torus, which we called ''Keplerian torus'', since it is a generalization of the Keplerian disk.
5. It is shown in the framework of the N-body problem that the geometric thickness of the torus is larger if, in the initial conditions for the particle orbits, we introduce a distribution of both inclination and eccentricity. It is shown that the equilibrium distribution of clouds in the torus, achieved due to self-gravity, satisfies the conditions of obscuration of the accretion disk in the AGNs. It is shown that the observed dynamics in NGC 1068 can be explained by the peculiarities of the cloud motions in the torus due to the effects of self-gravity. Temperature of clouds as a result of heating by radiation of the accretion disk are obtained, which satisfy the observational data in IR band.
6. The effects of gravitational lensing on the system of a central mass and of a torus (in the approach of a thin disk with a hole) have been investigated. It is shown that in this system the formation of three Einstein rings is possible. Two Einstein rings arise in a wide range of parameters with significantly different brightness. One Einstein ring is also formed, which can be identical to the case of lensing by a point mass, or, on the contrary, it may have a substantial width and high brightness.
7. It is shown that there are both analogies and qualitative differences in the dynamics of dipole toroidal vortexes in 3D from the behavior of vortex systems in the 2D case. In the convergent (accretion) flow, rings as well as their flat analogues are accelerated. In the case of a dipole toroidal vortex, this result leads to the component acceleration but the vortexes can collapse for some value of the flow power. It is shown that the integral of helicity for a toroidal vortex with a twist and a maximum of the velocity on the vortex generatrix is different from the known Moffat formula on the numerical coefficient.
8. It is shown that a problem of a pair of vortexes in a radial flow (in 2D case) allows an exact solution. In the converging flow, the vortexes in the pair approach each other with increasing speed. The dynamics of a dipole toroidal vortex in a radial flow in the approximation of four flat vortexes is considered. It is shown that in this case, the pair components are ejected by the convergent flow with exponentially increasing speed. It is shown that the main result associated with the acceleration of the outflows is kept for a more complicated flow (source and dipole, quadrupole), since the main influence has a monopole component of flow.
