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Mathematics of Nonlinear Science

Edited by: Melvyn S. Berger
Available Formats:
Electronic ISBN: 978-0-8218-7696-1
Product Code: CONM/108.E
List Price: $44.00 MAA Member Price:$39.60
AMS Member Price: $35.20 Click above image for expanded view Mathematics of Nonlinear Science Edited by: Melvyn S. Berger Available Formats:  Electronic ISBN: 978-0-8218-7696-1 Product Code: CONM/108.E  List Price:$44.00 MAA Member Price: $39.60 AMS Member Price:$35.20
• Book Details

Contemporary Mathematics
Volume: 1081990; 153 pp
MSC: Primary 70; 00; Secondary 34; 35; 49; 58;

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.

• Articles
• Roger K. Alexander - Multiple steady states in tubular chemical reactors [ MR 1068329 ]
• M. S. Berger - Two new approaches to large amplitude quasi-periodic motions of certain nonlinear Hamiltonian systems [ MR 1068330 ]
• Y. Y. Chen - Vortices for the Ginzburg-Landau equations—the nonsymmetric case in bounded domain [ MR 1068331 ]
• Andrew Szeri and Philip Holmes - Nonlinear stability and bifurcation in Hamiltonian systems with symmetry [ MR 1068332 ]
• Eli Isaacson and Blake Temple - Nonlinear resonance in inhomogeneous systems of conservation laws [ MR 1068333 ]
• George H. Knightly and D. Sather - Bifurcation and stability problems in rotating plane Couette-Poiseuille flow [ MR 1068334 ]
• Kenneth R. Meyer and Dieter S. Schmidt - Bifurcations of central configurations in the $N$-body problem [ MR 1068335 ]
• M. S. Berger and J. Nee - Leapfrogging of vortex filaments in an ideal fluid [ MR 1068336 ]
• J. W. Neuberger - Calculation of sharp shocks using Sobolev gradients [ MR 1068337 ]
• John Palmer and Craig A. Tracy - Monodromy preserving deformation of the Dirac operator acting on the hyperbolic plane [ MR 1068338 ]
• M. S. Berger and M. Schechter - Bifurcation from equilibria for certain infinite-dimensional dynamical systems [ MR 1068339 ]
• Victor Shubov - On dynamics of discrete and continuous $\sigma$-models (chiral fields) with values in Riemannian manifolds [ MR 1068340 ]
• Srdjan Stojanovic - Direct study for some nonlinear elliptic control problems [ MR 1068341 ]
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Volume: 1081990; 153 pp
MSC: Primary 70; 00; Secondary 34; 35; 49; 58;

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.

• Articles
• Roger K. Alexander - Multiple steady states in tubular chemical reactors [ MR 1068329 ]
• M. S. Berger - Two new approaches to large amplitude quasi-periodic motions of certain nonlinear Hamiltonian systems [ MR 1068330 ]
• Y. Y. Chen - Vortices for the Ginzburg-Landau equations—the nonsymmetric case in bounded domain [ MR 1068331 ]
• Andrew Szeri and Philip Holmes - Nonlinear stability and bifurcation in Hamiltonian systems with symmetry [ MR 1068332 ]
• Eli Isaacson and Blake Temple - Nonlinear resonance in inhomogeneous systems of conservation laws [ MR 1068333 ]
• George H. Knightly and D. Sather - Bifurcation and stability problems in rotating plane Couette-Poiseuille flow [ MR 1068334 ]
• Kenneth R. Meyer and Dieter S. Schmidt - Bifurcations of central configurations in the $N$-body problem [ MR 1068335 ]
• M. S. Berger and J. Nee - Leapfrogging of vortex filaments in an ideal fluid [ MR 1068336 ]
• J. W. Neuberger - Calculation of sharp shocks using Sobolev gradients [ MR 1068337 ]
• John Palmer and Craig A. Tracy - Monodromy preserving deformation of the Dirac operator acting on the hyperbolic plane [ MR 1068338 ]
• M. S. Berger and M. Schechter - Bifurcation from equilibria for certain infinite-dimensional dynamical systems [ MR 1068339 ]
• Victor Shubov - On dynamics of discrete and continuous $\sigma$-models (chiral fields) with values in Riemannian manifolds [ MR 1068340 ]
• Srdjan Stojanovic - Direct study for some nonlinear elliptic control problems [ MR 1068341 ]
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