Cosmic evolution leads from symmetry to complexity by symmetry breaking and phase transitions. The emergence of new order and structure in nature and society is explained by physical, chemical, biological, social and economic self-organization, according to the laws of nonlinear dynamics. All these dynamical systems are considered computational systems processing information and entropy. Are symmetry and complexity only useful models of science or are they universals of reality? Symmetry and Complexity discusses the fascinating insights gained from natural, social and computer sciences,...

Focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. This book extends the classical Melnikov's approach to the study of high dimensional dynamical systems.