Approximate dynamics of dark matter ellipsoids

The collapse of non-collisional dark matter and the formation of pancake structures in the Universe are investigated approximately. Collapse is described by a system of ordinary differential equations, in the model of a uniformly rotating, three-axis, uniform density ellipsoid. Violent relaxation, mass and angular momentum losses are taken into account phenomenologically. The formation of the equilibrium configuration, secular instability and the transition from a spheroid to a three-axis ellipsoid are investigated numerically and analytically in this dynamical model.Comment: 11 pages, 8 figure

Dynamical chaos in the problem of magnetic jet collimation

We investigate dynamics of a jet collimated by magneto-torsional oscillations. The problem is reduced to an ordinary differential equation containing a singularity and depending on a parameter. We find a parameter range for which this system has stable periodic solutions and study bifurcations of these solutions. We use Poincar\'e sections to demonstrate existence of domains of regular and chaotic motions. We investigate transition from periodic to chaotic solutions through a sequence of period doublings.Comment: 11 pages, 29 figures, 1 table, MNRAS (published online

Gravitational lensing by gravitational waves

Gravitational lensing by gravitational wave is considered. We notice that although final and initial direction of photons coincide, displacement between final and initial trajectories occurs. This displacement is calculated analytically for the plane gravitational wave pulse. Estimations for observations are discussed.Comment: 9 pages, 3 figure

Dynamic stabilization of non-spherical bodies against unlimited collapse

We solve equations, describing in a simplified way the newtonian dynamics of a selfgravitating nonrotating spheroidal body after loss of stability. We find that contraction to a singularity happens only in a pure spherical collapse, and deviations from the spherical symmetry stop the contraction by the stabilising action of nonlinear nonspherical oscillations. A real collapse happens after damping of the oscillations due to energy losses, shock wave formation or viscosity. Detailed analysis of the nonlinear oscillations is performed using a Poincar\'{e} map construction. Regions of regular and chaotic oscillations are localized on this map.Comment: MNRAS, accepted, 7 pages, 9 figure

Primordial Black Hole: Mass and Angular Momentum Evolution

The evolution of the primordial low mass black hole (PBH) in hot universe is considered. Increase of mass and decrease of PBH spin due to the accretion of radiation dominated matter are estimated with using of results of numerical simulation of PBH formation and approximate relations for accretion to a rotating black hole.Comment: Gravitation and Cosmology, accepted, 3 pages, Talk presented at the russian summer school-seminar "Modern theoretical problems of gravitation and cosmology" (GRACOS-2007), September 9-16, 2007, Kazan-Yalchik, Russi