TY - BOOK ID - 14307481 TI - Asymptotic solutions of strongly nonlinear systems of differential equations AU - Kozlov, V. V. AU - Furta, Stanislav D. PY - 2013 SN - 14397382 SN - 364233816X 3642432409 3642338178 1299197701 PB - Berlin : Springer, DB - UniCat KW - Differential equations, Nonlinear. KW - Geometry, Differential. KW - Nonlinear wave equations. KW - Differential equations KW - Mathematics KW - Physical Sciences & Mathematics KW - Calculus KW - Asymptotic theory KW - Asymptotic theory. KW - 517.91 Differential equations KW - Mathematics. KW - Dynamics. KW - Ergodic theory. KW - Differential equations. KW - Physics. KW - Ordinary Differential Equations. KW - Dynamical Systems and Ergodic Theory. KW - Mathematical Methods in Physics. KW - Differential Equations. KW - Differentiable dynamical systems. KW - Mathematical physics. KW - Physical mathematics KW - Physics KW - Differential dynamical systems KW - Dynamical systems, Differentiable KW - Dynamics, Differentiable KW - Global analysis (Mathematics) KW - Topological dynamics KW - Natural philosophy KW - Philosophy, Natural KW - Physical sciences KW - Dynamics KW - Ergodic transformations KW - Continuous groups KW - Mathematical physics KW - Measure theory KW - Transformations (Mathematics) KW - Dynamical systems KW - Kinetics KW - Mechanics, Analytic KW - Force and energy KW - Mechanics KW - Statics UR - https://www.unicat.be/uniCat?func=search&query=sysid:14307481 AB - 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. ER -