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Multiparameter Bifurcation Theory
 
Multiparameter Bifurcation Theory
eBook ISBN:  978-0-8218-7643-5
Product Code:  CONM/56.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Multiparameter Bifurcation Theory
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Multiparameter Bifurcation Theory
eBook ISBN:  978-0-8218-7643-5
Product Code:  CONM/56.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 561986; 387 pp
    MSC: Primary 58; Secondary 00

    This 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This proceedings volume demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields. Various papers study steady state bifurcation, Hopf bifurcation to periodic solutions, interactions between modes, dynamic bifurcations, and the role of symmetries in such systems. A section of abstracts at the end of the volume provides guides and pointers to the literature.

    The mathematical study of multiparameter bifurcation leads to a number of theoretical and practical difficulties, many of which are discussed in these papers. The articles also describe theoretical and experimental studies of chemical reactors, which provide many situations in which to test the mathematical ideas. Other test areas are found in fluid dynamics, particularly in studying the routes to chaos in two laboratory systems, Taylor-Couette flow between rotating cylinders and Rayleigh-Benard convection in a fluid layer.

  • Table of Contents
     
     
    • Articles
    • F. H. Busse — Phase-turbulence in convection near threshold
    • Shui-Nee Chow and Duo Wang — Normal forms of bifurcating periodic orbits [ MR 855081 ]
    • P. Coullet, D. Repaux and J. M. Vanel — Quasiperiodic Patterns
    • Richard Cushman and Jan A. Sanders — Nilpotent normal forms and representation theory of ${\rm sl}(2,{\bf R})$ [ MR 855083 ]
    • G. Dangelmayr and D. Armbruster — Steady-state mode interactions in the presence of ${\rm O}(2)$-symmetry and in nonflux boundary value problems [ MR 855084 ]
    • M. J. Field — Equivariant dynamics [ MR 855085 ]
    • Terence Gaffney — New methods in the classification theory of bifurcation problems [ MR 855086 ]
    • Stephan A. van Gils and Emil Horozov — Uniqueness of limit cycles in planar vector fields which leave the axes invariant [ MR 855087 ]
    • Martin Golubitsky and Ian Stewart — Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators [ MR 855088 ]
    • John Guckenheimer — A codimension two bifurcation with circular symmetry [ MR 855089 ]
    • Jack K. Hale — Local flows for functional-differential equations [ MR 855090 ]
    • E. Knobloch — On the degenerate Hopf bifurcation with ${\rm O}(2)$ symmetry [ MR 855091 ]
    • Edgar Knobloch, Anil E. Deane, Juri Toomre and Daniel R. Moore — Doubly diffusive waves [ MR 855092 ]
    • Reiner Lauterbach — An example of symmetry breaking with submaximal isotropy subgroup [ MR 855093 ]
    • Irene M. Moroz — Codimension-three bifurcations arising in Langmuir circulations [ MR 855094 ]
    • Wayne Nagata — Symmetric Hopf bifurcations and magnetoconvection [ MR 855095 ]
    • M. R. E. Proctor — Columnar convection in double-diffusive systems [ MR 855096 ]
    • Ingo Rehberg and Guenter Ahlers — Codimension two bifurcation in a convection experiment [ MR 855097 ]
    • Mark Roberts, James W. Swift and David H. Wagner — The Hopf bifurcation on a hexagonal lattice [ MR 855098 ]
    • D. H. Sattinger — Completely integrable Hamiltonian systems on semisimple Lie algebras [ MR 855099 ]
    • Lawrence Turyn — Bifurcation without mixed mode solutions [ MR 855100 ]
    • A. Vanderbauwhede — Hopf bifurcation at nonsemisimple eigenvalues [ MR 855101 ]
    • Pascal Chossat — Interaction of Azimuthal Modes in the Couette-Taylor Problem
    • T. Erneux and L. E. — Slowly Varying Bifurcation Parameters
    • B. F. Gray — Applications of Singularity Theory of Explosion Theory
    • P. C. Hohenberg, G. Ahlers and M. Lücke — Externally Modulated Convection Theory and Experiment
    • W. F. Langford — Equivariant Normal Forms for the Taylor-Couette Problem
    • S. Leibovich, S. K. Lele and I. M. Moroz — Development of Spatial and Temporal Complexity in Langmuir Circulation
    • Dan Luss — Steady-State Multiplicity Features of Chemically Reacting Systems
    • Kenneth R. Meyer — Bibliographic notes on generic bifurcations in Hamiltonian systems [ MR 855102 ]
    • Randall Tagg — Multicritical points in flow between independently rotating cylinders
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 561986; 387 pp
MSC: Primary 58; Secondary 00

This 1985 AMS Summer Research Conference brought together mathematicians interested in multiparameter bifurcation with scientists working on fluid instabilities and chemical reactor dynamics. This proceedings volume demonstrates the mutually beneficial interactions between the mathematical analysis, based on genericity, and experimental studies in these fields. Various papers study steady state bifurcation, Hopf bifurcation to periodic solutions, interactions between modes, dynamic bifurcations, and the role of symmetries in such systems. A section of abstracts at the end of the volume provides guides and pointers to the literature.

The mathematical study of multiparameter bifurcation leads to a number of theoretical and practical difficulties, many of which are discussed in these papers. The articles also describe theoretical and experimental studies of chemical reactors, which provide many situations in which to test the mathematical ideas. Other test areas are found in fluid dynamics, particularly in studying the routes to chaos in two laboratory systems, Taylor-Couette flow between rotating cylinders and Rayleigh-Benard convection in a fluid layer.

  • Articles
  • F. H. Busse — Phase-turbulence in convection near threshold
  • Shui-Nee Chow and Duo Wang — Normal forms of bifurcating periodic orbits [ MR 855081 ]
  • P. Coullet, D. Repaux and J. M. Vanel — Quasiperiodic Patterns
  • Richard Cushman and Jan A. Sanders — Nilpotent normal forms and representation theory of ${\rm sl}(2,{\bf R})$ [ MR 855083 ]
  • G. Dangelmayr and D. Armbruster — Steady-state mode interactions in the presence of ${\rm O}(2)$-symmetry and in nonflux boundary value problems [ MR 855084 ]
  • M. J. Field — Equivariant dynamics [ MR 855085 ]
  • Terence Gaffney — New methods in the classification theory of bifurcation problems [ MR 855086 ]
  • Stephan A. van Gils and Emil Horozov — Uniqueness of limit cycles in planar vector fields which leave the axes invariant [ MR 855087 ]
  • Martin Golubitsky and Ian Stewart — Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators [ MR 855088 ]
  • John Guckenheimer — A codimension two bifurcation with circular symmetry [ MR 855089 ]
  • Jack K. Hale — Local flows for functional-differential equations [ MR 855090 ]
  • E. Knobloch — On the degenerate Hopf bifurcation with ${\rm O}(2)$ symmetry [ MR 855091 ]
  • Edgar Knobloch, Anil E. Deane, Juri Toomre and Daniel R. Moore — Doubly diffusive waves [ MR 855092 ]
  • Reiner Lauterbach — An example of symmetry breaking with submaximal isotropy subgroup [ MR 855093 ]
  • Irene M. Moroz — Codimension-three bifurcations arising in Langmuir circulations [ MR 855094 ]
  • Wayne Nagata — Symmetric Hopf bifurcations and magnetoconvection [ MR 855095 ]
  • M. R. E. Proctor — Columnar convection in double-diffusive systems [ MR 855096 ]
  • Ingo Rehberg and Guenter Ahlers — Codimension two bifurcation in a convection experiment [ MR 855097 ]
  • Mark Roberts, James W. Swift and David H. Wagner — The Hopf bifurcation on a hexagonal lattice [ MR 855098 ]
  • D. H. Sattinger — Completely integrable Hamiltonian systems on semisimple Lie algebras [ MR 855099 ]
  • Lawrence Turyn — Bifurcation without mixed mode solutions [ MR 855100 ]
  • A. Vanderbauwhede — Hopf bifurcation at nonsemisimple eigenvalues [ MR 855101 ]
  • Pascal Chossat — Interaction of Azimuthal Modes in the Couette-Taylor Problem
  • T. Erneux and L. E. — Slowly Varying Bifurcation Parameters
  • B. F. Gray — Applications of Singularity Theory of Explosion Theory
  • P. C. Hohenberg, G. Ahlers and M. Lücke — Externally Modulated Convection Theory and Experiment
  • W. F. Langford — Equivariant Normal Forms for the Taylor-Couette Problem
  • S. Leibovich, S. K. Lele and I. M. Moroz — Development of Spatial and Temporal Complexity in Langmuir Circulation
  • Dan Luss — Steady-State Multiplicity Features of Chemically Reacting Systems
  • Kenneth R. Meyer — Bibliographic notes on generic bifurcations in Hamiltonian systems [ MR 855102 ]
  • Randall Tagg — Multicritical points in flow between independently rotating cylinders
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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