Nonlinear Dynamics: A Primer

by Alfredo Medio, Marji Lines

Overview

This textbook on the theory of nonlinear dynamical systems for nonmathematical advanced undergraduate or graduate students is also a reference book for researchers in the physical and social sciences. It provides a comprehensive introduction including linear systems, stability theory of nonlinear systems, bifurcation theory, chaotic dynamics. Discussion of the measure--theoretic approach to dynamical systems and the relation between deterministic systems and stochastic processes is featured. There are a hundred exercises and an associated website provides a software program, computer exercises and answers to selected book exercises.

Product Details

ISBN-13:	9780521558747
Publisher:	Cambridge University Press
Publication date:	10/11/2001
Edition description:	New Edition
Pages:	316
Product dimensions:	6.69(w) x 9.61(h) x 0.67(d)

About the Author

Alfredo Medio is currently Professor of Mathematical Economics at the University 'Ca' Foscari' of Venice and Director of the International Center of Economics and Finance at the Venice International University. After receiving a Ph.D. in Economics from Cambridge University he taught at several universities around the world, including the New School for Social Research (New York), the Ecole of Hautes Etudes in Sciences Sociales (Marseilles), Duke University and the University of Paris. He also served as Economic Affairs Officer of UNCTAD (Geneva). Professor Medio is the author of numerous articles published in learned journals and of the book Chaotic Dynamics: Theory and Applications to Economics (Cambridge University Press, 1992).

Marji Lines is currently Associate Professor of Economics at the University of Udine (Italy). Since completing a Ph.D. in Economics at the University of Utah (Salt Lake City), she has taught courses in Economics, Econometrics and Mathematical Economics, principally at the University of Udine, but also at Duke University (Durham, NC) and Deakin University (Melbourne). She has been a Visiting Scholar at the Santa Fe Institute and the Faculty of Economics and Politics, Cambridge University and has published articles on economic theory and environmental economics in journals and collections.

Table of Contents

1. Statics and dynamics: some elementary concepts; 2. Review of linear systems; 3. Stability of fixed points; 4. Invariant and attracting sets, periodic and quasiperiodic orbits; 5. Local bifurcations; 6. Chaotic sets and chaotic attractors; 7. Characteristic exponents, fractals, homoclinic orbits; 8. Transition to chaos; 9. The ergodic approach; 10. Deterministic systems and stochastic processes.

Editorial Reviews

'… the book is well written and contains lots of useful information. It will serve as a good reference on dynamical systems both for students and researchers.' Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts

From the Publisher

Writing for economics students and other non-mathematical students, Medio (mathematical economics, Universit<`a> Ca' Foscari di Venezia, Italy) and Lines (economics, Universit<`a> di Udine, Italy) introduce the study of nonlinear dynamical studies. Results deemed most relevant for applications are the focus of the work, which passes over much of the more specialized portions of the field. Significant time is spent on a discussion of stability and attention is paid to chaotic sets and attractors. Specific applications are largely ignored with the material veering more towards theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)