Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations - Kozlov, Valery V.; Furta, Stanislav D.; SpringerLink (Online service) (Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013)
The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunov$1 (Bs first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in the strongly nonlinear case, where the existence of such solutions can$1 (Bt be inferred on the basis of the first approximation alone. The book is illustrated with a large number of concrete examples of systems in which the presence of a particular solution of a certain class is related to special properties of the system$1 (Bs dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.s
Preface -- Semi-quasihomogeneous systems of ordinary differential equations -- 2. The critical case of purely imaginary kernels -- 3. Singular problems -- 4. The inverse problem for the Lagrange theorem on the stability of equilibrium and other related problems -- Appendix A. Nonexponential asymptotic solutions of systems of functional-differential equations -- Appendix B. Arithmetic properties of the eigenvalues of the Kovalevsky matrix and conditions for the nonintegrability of semi-quasihomogeneous systems of ordinary dierential equations -- Bibliography.
Keywords: Mathematics; Differentiable dynamical systems; Differential Equations; Mathematical physics; Mathematics; Ordinary Differential Equations; Dynamical Systems and Ergodic Theory; Mathematical Methods in Physics