Differential Dynamical Systems

In recent years there has been unprecedented popular interest in the chaotic behaviour of discrete dynamical systems.

Introduction to conjugacy problems for difieomorphisms. This is a survey article on the area of global analysis defined by differentiable dynamical systems or equivalently the action (differentiable) of a Lie group G on a manifold M. An action is a homomorphism G-Diff(M) such that the induced map GXM-M is differentiable. Here Diff(M) is the group of all diffeomorphisms of M and a diffeomorphism is a differentiable map with a differentiable inverse. Everything will be discussed here from the C«> or C" point of view. All manifolds maps, etc. will be differentiable (Cr, 1;;:; r ~ 00) unless stated otherwise.

This book presents recent developments in nonlinear dynamics and physics with an emphasis on complex systems. The contributors provide recent theoretic developments and new techniques to solve nonlinear dynamical systems and help readers understand complexity, stochasticity, and regularity in nonlinear dynamical systems.

This book contains a systematic study of autonomous systems of ordinary differential equations and dynamical systems. It begins with a thorough treatment of linear systems; however, the main topic of the book is local and global behavior of nonlinear systems.