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Dynamical Systems and Probabilistic Methods in Partial Differential Equations
Edited by: Percy Deift, New York University, Courant Institute, NY, C. David Levermore, University of Arizona, Tucson, AZ, and C. Eugene Wayne, Pennsylvania State University, University Park, PA

Lectures in Applied Mathematics
1996; 268 pp; softcover
Volume: 31
Reprint/Revision History:
reprinted 1998
ISBN-10: 0-8218-0368-9
ISBN-13: 978-0-8218-0368-4
List Price: US$36
Member Price: US$28.80
Order Code: LAM/31
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This volume contains some of the lectures presented in June 1994 during the AMS-SIAM Summer Seminar at the Mathematical Sciences Research Institute in Berkeley. The goal of the seminar was to introduce participants to as many interesting and active applications of dynamical systems and probabilistic methods to problems in applied mathematics as possible. As a result, this book covers a great deal of ground. Nevertheless, the pedagogical orientation of the lectures has been retained, and therefore the book will serve as an ideal introduction to these varied and interesting topics.

Among the themes explored in this volume are the following:

  • the increasing role of dynamical systems theory in understanding partial differential equations
  • the central importance of certain prototypical equations, such as the complex Ginzburg-Landau, nonlinear Schrödinger, and Korteweg-deVries equations
  • problems in fluid mechanics and the limits of physically motivated heuristic theories of fluids
  • the role of probabilistic methods in studying turbulent phenomena


Researchers in applied mathematics.

Table of Contents

Section I: Dynamical Systems and PDEs
  • C. E. Wayne -- An introduction to KAM theory
  • W. Craig -- KAM theory in infinite dimensions
  • N. Kopell -- Global center manifolds and singularly perturbed equations: A brief (and biased) guide to (some of) the literature
  • D. W. McLaughlin and J. Shatah -- Melnikov analysis for PDE's
Section II: Exactly Integrable Systems
  • P. Deift -- Integrable Hamiltonian systems
Section III: Amplitude Equations
  • C. D. Levermore and M. Oliver -- The complex Ginzburg-Landau equation as a model problem
  • A. Mielke and G. Schneider -- Derivation and justification of the complex Ginzburg-Landau equation as a modulation equation
Section IV: Fluid Mechanics and Turbulence
  • P. Constantin -- Navier-Stokes equations and incompressible fluid turbulence
  • A. J. Chorin -- Turbulence as a near-equilibrium process
  • M. Avellaneda -- Homogenization and renormalization: The mathematics of multi-scale random media and turbulent diffusion
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