From the reviews:
“This remarkable collection comprises a selection of the more mathematically oriented articles from the enormous Encyclopedia of complexity and systems science. … The articles have been carefully edited … with a glossary of key terms, careful exposition, and a substantial specialised bibliography … . For a reasonably mathematically sophisticated reader, this will provide a good introduction to new areas, and the high quality of writing and editing means that one would be confident pointing researchers or undergraduates doing projects in related areas to this collection.” (Thomas B. Ward, Zentralblatt MATH, Vol. 1236, 2012)
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic.
The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifracticals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.