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Mathematics of Nonlinear Science
Edited by: Melvyn S. Berger
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Contemporary Mathematics
1990; 153 pp; softcover
Volume: 108
ISBN-10: 0-8218-5114-4
ISBN-13: 978-0-8218-5114-2
List Price: US$44 Member Price: US$35.20
Order Code: CONM/108

This volume contains the proceedings of an AMS Special Session on the Mathematics of Nonlinear Science, held in Phoenix in January 1989. This area of research encompasses a large and rapidly growing set of ideas concerning the relationship of mathematics to science, in which the fundamental laws of nature are extended beyond common sense into new areas where the dual aspects of order and chaos abound.

These papers, generally analytic in nature, deal primarily with mathematical aspects of physical science and non-chaotic phenomenon. Important new areas are discussed, such as instability, global extensions of KAM theory, new ideas concerning integrable systems, bifurcation and its applications in fluids, and various aspects of gauge theory. Altogether, the topics explored here represent an excellent survey of some of the new research in the mathematics of nonlinear science.

• R. K. Alexander -- Multiple steady states in tubular chemical reactors
• M. S. Berger -- Two new approaches to large amplitude quasi-periodic motions of certain nonlinear Hamiltonian systems
• Y. Y. Chen -- Vortices for the Ginzburg-Landau equations-the nonsymmetric case in bounded domain
• A. Szeri and P. Holmes -- Nonlinear stability and bifurcation in Hamiltonian systems with symmetry
• E. Isaacson and B. Temple -- Nonlinear resonance in inhomogeneous systems of conservation laws
• G. H. Knightly and D. Sather -- Bifurcation and stability in rotating, plane Couette-Poiseuille flow
• K. R. Meyer and D. S. Schmidt -- Bifurcations of central configurations in the $$N$$-body problem
• M. S. Berger and J. Nee -- Leapfrogging of vortex filaments in an ideal fluid
• J. W. Neuberger -- Calculation of sharp shocks using Sobolev gradients
• J. Palmer and C. A. Tracy -- Monodromy preserving deformation of the Dirac operator acting on the hyperbolic plane
• M. S. Berger and M. Schechter -- Bifurcation from equilibria for certain infinite-dimensional dynamical systems
• V. Shubov -- On dynamics of discrete and continuous $$\sigma$$-models (chiral fields) with values in Riemannian manifolds
• S. Stojanovic -- Direct study for some nonlinear elliptic control problems