Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations

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’s 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’t 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’s dynamic behavior. It is a book for students and specialists who work with dynamical systems in the fields of mechanics, mathematics, and theoretical physics.

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 di¤erential equations.- Bibliography.