Method of Averaging for Differential Equations on an Infinite Interval. Theory and Applications
This is a very readable book introducing the reader to the method of averaging for systems of ordinary differential equations with almost periodic right hand sides and a small parameter. The existence of almost periodic solutions and stability of equilibria are investigated in detail. Abstract results are applied to concrete equations (such as a general pendulum, van der Pohl and Duffing’s equation and the Hopf bifurcation). Equations having slow and fast time are also studied. The book is divided into two parts; the first one describes averaging for linear systems and the second one is devoted to nonlinear systems. There are also three short appendices on almost periodic functions, the Lyapunov first and second methods and basic facts of functional analysis. This clearly written book can be highly recommended to students with interests in ordinary differential equations. Non-experts and researchers in natural sciences will also find interesting methods that are useful in applications.