Nonlinear Mechanics, Groups and Symmetry

Inhaltsverzeichnis

• 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.