Dynamical Systems, Graphs, and Algorithms (Lecture Notes in Mathematics, 1889) - Softcover

Osipenko, George

Softcover

ISBN 10: 3540355936 ISBN 13: 9783540355939

Publisher: Springer, 2006

Synopsis

This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.

About this title

About the Author

FRED NEUBAUER is Professor of Multinational Corporate Strategy and Planning at the International Institute for Management Development (IMD) in Lausanne, Switzerland. As well as having taught in the area of management all over the world, he has been a consultant to multinational corporations, many of them leading family-controlled enterprises. His main area of research is corporate governance and corporate boards in privately-held and publicly traded corporations. He is co-author of The Corporate Board: Confronting the Paradoxes.

ALDEN G. LANK is Stephen Schmidheiny Professor of Family Enterprises and Professor of Organizational Behaviour at the International Institute for Management Development (IMD) in Lausanne, Switzerland. At the IMD he is in charge of the Family Business Area and Director of the Leading the Family Business educational program. He is also President and member of the Executive Board of the Family Business Network and has served as a Board member of the Family Firm Institute and editorial board of the Family Business Review.

Review

From the reviews:

"This book provides a taster for using symbolic analysis, graph theory, and set-oriented methods in a quest to understand the global structure of the dynamics in a continuous- or discrete-time system. In many ways, the techniques discussed here are complementary to more traditional ways of analysing a dynamical system and as such, this book can be viewed as a valuable entry into the theory and computational methods. ... The book is intended for postgraduate researchers ... ." (Hinke M. Osinga, Mathematical Reviews, Issue 2008 i)

"This monograph contains a summary of the author’s work on constructive methods for the study of discrete dynamical systems. ... The structure of the book is very clear with 14 chapters devoted to different dynamical objects such as chain recurrent sets, structural stability or invariant manifolds, followed by two examples: the Ikeda mapping and a discrete food-chain model. ... is certainly a valuable and very readable reference, in particular for the study of low-dimensional concrete systems with complicated dynamics." (Jörg Härterich, Zentralblatt MATH, Vol. 1130 (8), 2008)

Edition details

• Publisher: Springer
• Publication date: 2006
• Language: English
• ISBN 10: 3540355936
• ISBN 13: 9783540355939
• Binding: Paperback
• Number of pages: 300