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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.

Differential equations, Nonlinear. --- Geometry, Differential. --- Nonlinear wave equations. --- Differential equations --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Asymptotic theory --- Asymptotic theory. --- 517.91 Differential equations --- Mathematics. --- Dynamics. --- Ergodic theory. --- Differential equations. --- Physics. --- Ordinary Differential Equations. --- Dynamical Systems and Ergodic Theory. --- Mathematical Methods in Physics. --- Differential Equations. --- Differentiable dynamical systems. --- Mathematical physics. --- Physical mathematics --- Physics --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Global analysis (Mathematics) --- Topological dynamics --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics