Physics of Gravitating Systems II

(Volume II).- Non-Jeans Instabilities of Gravitating Systems.- VI Non-Jeans Instabilities of Gravitating Systems.- 1. Beam Instability of a Gravitating Medium.- 1.1. Theorem of a Number of Instabilities of the Heterogeneous System with Homogeneous Flows.- 1.2. Expression for the Growth Rate of the Kinetic Beam Instability in the Case of a Beam of Small Density (for an Arbitrary Distribution Function).- 1.3. Beam with a Step Function Distribution.- 1.4. Hydrodynamical Beam Instability. Excitation of the Rotational Branch.- 1.5. Stabilizing Effect of the Interaction of Gravitating Cylinders and Disks.- 1.6. Instability of Rotating Inhomogeneous Cylinders with Oppositely Directed Beams of Equal Density.- 2. Gradient Instabilities of a Gravitating Medium.- 2.1. Cylinder of Constant Density with Radius-Dependent Temperature. Hydrodynamical Instability.- 2.2. Cylinder of Constant Density with a Temperature Jump. Kinetic Instability.- 2.3. Cylinder with Inhomogeneous Density and Temperature.- 3. Hydrodynamical Instabilities of a Gravitating Medium with a Growth Rate Much Greater than that of Jeans.- 3.1. Hydrodynamical Instabilities in the Model of a Flat Parallel Flow.- 3.2. Hydrodynamical Instabilities of a Gravitating Cylinder.- 4. General Treatment of Kinetic Instabilities.- 4.1. Beam Effects in the Heterogeneous Model of a Galaxy.- 4.2. Influence of a Black Hole at the Center of a Spherical System on the Resonance Interactions Between Stars and Waves.- 4.3. Beam Instability in the Models of a Cylinder and a Flat Layer.- VII Problems of Nonlinear Theory.- 1. Nonlinear Stability Theory of a Rotating, Gravitating Disk.- 1.1. Nonlinear Waves and Solitons in a Hydrodynamical Model of an Infinitely Thin Disk with Plane Pressure.- 1.2. Nonlinear Waves in a Gaseous Disk.- 1.3. Nonlinear Waves and Solitons in a Stellar Disk.- 1.4. Explosive Instability.- 1.5. Remarks on the Decay Processes.- 1.6. Nonlinear Waves in a Viscous Medium.- 2. Nonlinear Interaction of a Monochromatic Wave with Particles in Gravitating Systems.- 2.1. Nonlinear Dynamics of the Beam Instability in a Cylindrical Model.- 2.2. Nonlinear Saturation of the Instability at the Corotation Radiusin the Disk.- 3. Nonlinear Theory of Gravitational Instability of a Uniform Expanding Medium.- 4. Foundations of Turbulence Theory.- 4.1. Hamiltonian Formalism for the Hydrodynamical Model of a Gravitating Medium.- 4.2. Three-Wave Interaction.- 4.3. Four-Wave Interaction.- 5. Concluding Remarks.- 5.1. When Can an Unstable Gravitating Disk be Regarded as an Infinitesimally Thin One?.- 5.2. On Future Soliton Theory of Spiral Structure.- Problems.- II Astrophysical Applications.- VIII General Remarks.- 1. Oorts Antievolutionary Hypothesis.- 2. Is There a Relationship Between the Rotational Momentum of an Elliptical Galaxy and the Degree of Oblateness?.- 3. General Principles of the Construction of Models of Spherically Symmetric Systems.- 4. Lynden-Bells Collisionless Relaxation.- 5. Estimates of Collisionlessness of Particles in Different Real Systems.- IX Spherical Systems.- 1. A Brief Description of Observational Data.- 1.1. Globular Star Clusters.- 1.2. Spherical Galaxies.- 1.3. Compact Galactic Clusters.- 2. Classification of Unstable Modes in Scales.- 3. Universal Criterion of the Instability.- 4. Specificity of the Effects of Small-Scale and Large-Scale Perturbations on the Systems Evolution.- 5. Results of Numerical Experiments for Systems with Parameters Providing Strong Supercriticality.- 6. Example of Strongly Unstable Model.- 7. Can Lynden-Bells Intermixing Mechanism Be Observed Against a Background of Strong Instability ?.- 8. Is the Unstable Distribution of Stellar Density Really Unstable (in the Hydrodynamical Sense) in the Neighborhood of a Black Hole?.- X Ellipsoidal Systems.- 1. Objects Under Study.- 2. Elliptical Galaxies.- 2.1. Why Are Elliptical Galaxies More Oblate than E7 Absent?.- 2.2. Comparison of the