This paper aims at reviewing nonlinear methods for model order reduction in structures with
geometric nonlinearity, with a special emphasis on the techniques based on invariant …

Investigating the dynamics of a network of oscillatory systems is a timely and urgent topic.
Phase synchronization has proven paradigmatic to study emergent collective behavior …

In this book we will study equations of the following form x= f (x, t; µ),(0.0. 1) and x↦→ g (x;
µ),(0.0. 2) with x∈ U⊂ Rn, t∈ R1, and µ∈ V⊂ Rp where U and V are open sets in Rn and …

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 …

The theory of Hamiltonian systems is a vast subject which can be studied from many
different viewpoints. This book develops the basic theory of Hamiltonian differential …

Universitext Page 1 123 Universitext Qualitative Theory of Planar Differential Systems Freddy
Dumortier Jaume Llibre Joan C. Artés Page 2 Page 3 123 Freddy Dumortier, Jaume Llibre …

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied
mathematics and algebra, this book presents an innovative synthesis of methods used to …

This book is mainly concerned with the bifurcation theory of ODEs. Chapters 1 and 2 of the
book introduce two systematic methods of simplifying equations: center manifold theory and …

Pattern formation in physical systems is one of the major research frontiers of mathematics.
A central theme of this book is that many instances of pattern formation can be understood …