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With a pedagogic format ideal for graduate students, this text includes a wealth of examples focusing on solutions in dynamical systems theory that mirror those used in Lyapunov´s first method, tackling ordinary differential equations expressed as series form.

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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.

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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.

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