Introduction To The Modern Theory Of Dynamical Systems (Encyclopedia Of Mathematics And Its Applications, Series Number 54)

Introduction To The Modern Theory Of Dynamical Systems (Encyclopedia Of Mathematics And Its Applications, Series Number 54)

This book provides a self-contained comprehensive exposition of the theory of dynamical systems. The book begins with a discussion of several elementary but crucial examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate and up.Review"...well written and clear...a valuable reference for engineers and mechanicians." H.W. Haslach Jr., Applied Mechanics Reviews"The book is a pleasure to read." Edoh Amiran, Mathematical Reviews"The notes section at the end of the book is complete and quite helpful. There are hints and answers provided for a good percentage of the problems in the book. The problems range from fairly straightforward ones to results that I remember reading in research papers over the last 10-20 years....I recommend the text as an exceptional reference..." Richard Swanson, SIAM ReviewBook DescriptionA self-contained comprehensive introduction to the mathematical theory of dynamical systems for students and researchers in mathematics, science and engineering.From the Back CoverThis book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbits structure. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up. Scientists and engineers working in applied dynamics, nonlinear science, and chaos will also find many fresh insights in this concrete and clear presentation. It contains more than four hundred systematic exercises.