Handbook of Dynamical Systems - 1st Edition - ISBN: 9780444501684, 9780080532844

Handbook of Dynamical Systems, Volume 2

1st Edition

Editors: B. Fiedler
eBook ISBN: 9780080532844
Hardcover ISBN: 9780444501684
Imprint: North Holland
Published Date: 21st February 2002
Page Count: 1098
Tax/VAT will be calculated at check-out Price includes VAT (GST)
20% off
20% off
20% off
20% off
20% off
Price includes VAT (GST)

Easy - Download and start reading immediately. There’s no activation process to access eBooks; all eBooks are fully searchable, and enabled for copying, pasting, and printing.

Flexible - Read on multiple operating systems and devices. Easily read eBooks on smart phones, computers, or any eBook readers, including Kindle.

Open - Buy once, receive and download all available eBook formats, including PDF, EPUB, and Mobi (for Kindle).

Institutional Access

Secure Checkout

Personal information is secured with SSL technology.

Free Shipping

Free global shipping
No minimum order.

Table of Contents

A. Finite-Dimensional Methods

  1. Mechanisms of phase-locking and frequency control in pairs of coupled neural oscillators (N. Kopell, G.B. Ermentrout).
  2. Invariant manifolds and Lagrangian dynamics in the ocean and atmosphere (C. Jones, S. Winkler).
  3. Geometric singular perturbation analysis of neuronal dynamics (J.E. Rubin, D. Terman).

    B. Numerics

  4. Numerical continuation, and computation of normal forms (W.-J. Beyn, A. Champneys, E. Doedel, W. Govaerts,Y.A. Kuznetsov, B. Sandstede).

  5. Set oriented numerical methods for dynamical systems (M. Dellnitz, O. Junge).
  6. Numerics and exponential smallness (V. Gelfreich).
  7. Shadowability of chaotic dynamical systems (C. Grebogi, L. Poon, T. Sauer, J.A. Yorke, D. Auerbach).
  8. Numerical analysis of dynamical systems (J. Guckenheimer).

    C. Topological Methods

  9. Conley index (K. Mischaikow, M. Mrozek).

  10. Functional differential equations (R.D. Nussbaum).

    D. Partial Differential Equations

  11. Navier--Stokes equations and dynamical systems (C. Bardos, B. Nicolaenko).

  12. The nonlinear Schrödinger equation as both a PDE and a dynamical system (D. Cai, D.W. McLaughlin, K.T.R. McLaughlin).
  13. Pattern formation in gradient systems (P.C. Fife).
  14. Blow-up in nonlinear heat equations from the dynamical systems point of view (M. Fila, H. Matano).
  15. The Ginzburg--Landau equation in its role as a modulation equation (A. Mielke).
  16. Parabolic equations: asymptotic behavior and dynamics on invariant manifolds (P. Poláčik). 17.Global attractors in partial differential equations (G. Raugel).
  17. Stability of travelling waves (B. Sandstede).


This handbook is volume II in a series collecting mathematical state-of-the-art surveys in the field of dynamical systems. Much of this field has developed from interactions with other areas of science, and this volume shows how concepts of dynamical systems further the understanding of mathematical issues that arise in applications. Although modeling issues are addressed, the central theme is the mathematically rigorous investigation of the resulting differential equations and their dynamic behavior. However, the authors and editors have made an effort to ensure readability on a non-technical level for mathematicians from other fields and for other scientists and engineers.

The eighteen surveys collected here do not aspire to encyclopedic completeness, but present selected paradigms. The surveys are grouped into those emphasizing finite-dimensional methods, numerics, topological methods, and partial differential equations. Application areas include the dynamics of neural networks, fluid flows, nonlinear optics, and many others.

While the survey articles can be read independently, they deeply share recurrent themes from dynamical systems. Attractors, bifurcations, center manifolds, dimension reduction, ergodicity, homoclinicity, hyperbolicity, invariant and inertial manifolds, normal forms, recurrence, shift dynamics, stability, to name just a few, are ubiquitous dynamical concepts throughout the articles.


No. of pages:
© North Holland 2002
North Holland
eBook ISBN:
Hardcover ISBN:

About the Editors

B. Fiedler Editor

Affiliations and Expertise

Freie Universität Berlin, Institut für Mathematik I, Berlin, Germany