Handbook of Dynamical Systems (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
1098
Utgivningsdatum
2002-02-01
Förlag
North Holland
Medarbetare
Fiedler, B. (ed.)
Illustrationer
Illustrations (some col.)
Volymtitel
Vol 2 Towards Applications
Dimensioner
246 x 170 x 71 mm
Vikt
2247 g
Antal komponenter
1
ISSN
1874575X
ISBN
9780444501684

Handbook of Dynamical Systems

av B Fiedler
Inbunden,  Engelska, 2002-02-01
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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.
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Innehållsförteckning

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 Schrodinger 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. Polacik). 17.Global attractors in partial differential equations (G. Raugel). 18. Stability of travelling waves (B. Sandstede).

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