This book is devoted to background material and recently developed mathematical methods in the
study of infinite-dimensional dissipative systems. The theory of such systems is motivated by
the long-term goal to establish rigorous mathematical models for turbulent and chaotic
phenomena. The aim here is to offer general methods and abstract results pertaining to
fundamental dynamical systems properties related to dissipative long-time behavior. The book
systematically presents develops and uses the quasi-stability method while substantially
extending it by including for consideration new classes of models and PDE systems arising in
Continuum Mechanics. The book can be used as a textbook in dissipative dynamics at the graduate
level. Igor Chueshov is a Professor of Mathematics at Karazin Kharkov National University in
Kharkov Ukraine.
