Perturbation theory and in particular normal form theory has shown strong growth during the
last decades. So it is not surprising that we are presenting a rather drastic revision of the first …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Perturbation theory, one of the most intriguing and essential topics in mathematics, and its
applications to the natural and engineering sciences is the main focus of this workbook. In a …

Nonlinear resonance analysis is a unique mathematical tool that can be used to study
resonances in relation to, but independently of, any single area of application. This is the first …

Among the theoretical methods for solving many problems of applied mathematics, physics,
and technology, asymptotic methods often provide results that lead to obtaining more …

This book offers up novel research which uses analytical approaches to explore nonlinear
features exhibited by various dynamic processes. Relevant to disciplines across …

This primer on averaging theorems provides a practical toolbox for applied mathematicians,
physicists, and engineers seeking to apply the well-known mathematical theory to real-world …

We present and review results on the continuation and bifurcation of periodic solutions in
conservative, reversible and Hamiltonian systems in the presence of symmetries. In …

Scaling time and spatial domains often seem natural in ODEs, but unfortunately, its useful
explicit form does not always agree with intuition. After reviewing the well-known methods …

We present a global analysis of the centre manifold of the collinear points in the circular
restricted three-body problem. The phase-space structure is provided by a family of resonant …