Nonlinear Mechanics, Groups and Symmetry: Mathematics and Its Applications, cartea 319

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 systems 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.- A: Lie series and Lie transformation.- B: The direct product of matrices.- B1: Definition.- B2: Systems of matrix equations.- 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.- D1: One-parameter group and its infinitesimal operator.- D2. Theory of extension.- Bibliographical Comments.- References.