eBook ISBN:  9780821876435 
Product Code:  CONM/56.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821876435 
Product Code:  CONM/56.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 56; 1986; 387 ppMSC: 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, TaylorCouette flow between rotating cylinders and RayleighBenard convection in a fluid layer.

Table of Contents

Articles

F. H. Busse — Phaseturbulence in convection near threshold

ShuiNee 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 — Steadystate 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 functionaldifferential 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 — Codimensionthree bifurcations arising in Langmuir circulations [ MR 855094 ]

Wayne Nagata — Symmetric Hopf bifurcations and magnetoconvection [ MR 855095 ]

M. R. E. Proctor — Columnar convection in doublediffusive 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 CouetteTaylor 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 TaylorCouette Problem

S. Leibovich, S. K. Lele and I. M. Moroz — Development of Spatial and Temporal Complexity in Langmuir Circulation

Dan Luss — SteadyState 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


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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, TaylorCouette flow between rotating cylinders and RayleighBenard convection in a fluid layer.

Articles

F. H. Busse — Phaseturbulence in convection near threshold

ShuiNee 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 — Steadystate 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 functionaldifferential 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 — Codimensionthree bifurcations arising in Langmuir circulations [ MR 855094 ]

Wayne Nagata — Symmetric Hopf bifurcations and magnetoconvection [ MR 855095 ]

M. R. E. Proctor — Columnar convection in doublediffusive 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 CouetteTaylor 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 TaylorCouette Problem

S. Leibovich, S. K. Lele and I. M. Moroz — Development of Spatial and Temporal Complexity in Langmuir Circulation

Dan Luss — SteadyState 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