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| HANDBOOK OF DYNAMICAL SYSTEMS, VOLUME 2
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Edited By
B. Fiedler, Freie Universität Berlin, Institut für Mathematik I, Berlin, Germany
Description
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.
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).
18. Stability of travelling waves (B.
Sandstede).
| Bibliographic details |
Hardbound, 1098 pages, publication date: FEB-2002
ISBN-13: 978-0-444-50168-4
ISBN-10: 0-444-50168-1
Imprint: NORTH-HOLLAND
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| Price and Ordering |
Price:
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EUR 210.95
GBP 179
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Last update: 3 Oct 2009
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