Nonlinear Mechanics, Groups and Symmetry

Introduction. 1. Vector Fields, Algebras and Groups Generated by a System of Ordinary Differential Equations and their Properties. 2. Decomposition of Systems of Ordinary Differential Equations. 3. Asymptotic Decomposition of Ordinary Differential Equations with a Small Parameter. 4. Asymptotic Decomposition of Almost Linear Systems of Differential Equations with Constant Coefficients and Perturbations in the Form of Polynomials. 5. Asymptotic Decomposition of Differential Systems with Small Parameter in the Representation Space of Finite-Dimensional Lie Group. 6. Asymptotic Decomposition of Differential Systems where Zero Approximation has Special Properties. 7. Asymptotic Decomposition of Pfaffian Systems with a Small Parameter. Appendix: A: Lie Series and Lie Transformation. B: The Direct Product of Matrices. C: Conditions for the Solvability of Systems of Linear Equations. D: Elements of Lie Group Analysis of Differential Equations on the Basis of the Theory of Extended Operators. Bibliographical Comments. References. Index.