Multiparameter bifurcation theory : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 14-20, 1985, with support from the National Science Foundation
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書誌事項
Multiparameter bifurcation theory : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 14-20, 1985, with support from the National Science Foundation
（Contemporary mathematics, v. 56）
American Mathematical Society, c1986
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注記
Includes bibliographies
"The AMS-IMS-SIAM Joint Summer Research Conference in the Mathematical Sciences on Multiparameter Bifurcation Theory was held at Humboldt State University, Arcata, California on July 14-20, 1985 with support from the National Science Foundation, Grant DMS-8415201"--T.p. verso
内容説明・目次
内容説明
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 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.
目次
Contributed Papers: Phase-turbulence in convection near threshold by F. H. Busse Normal forms of bifurcating periodic orbits by S.-N. Chow and D. Wang Quasiperiodic patterns by P. Coullet, D. Repaux, and J. M. Vanel Nilpotent normal forms and representation theory of $s1(2,\mathb{R})$ by R. Cushman and J. A. Sanders Steady-state mode interactions in the presence of $O(2)$-symmetry and in non-flux boundary value problems by G. Dangelmayr and D. Armbruster Equivariant dynamics by M. J. Field Some new results in the classification theory of bifurcation problems by T. Gaffney Uniqueness of limit cycles in planar vector fields which leave the axes invariant by S. A. van Gils and E. Horozov Hopf bifurcation with dihedral group symmetry: coupled nonlinear oscillators by M. Golubitsky and I. Stewart A codimension two bifurcation with circular symmetry by J. Gukenheimer Local flows for functional differential equations by J. K. Hale On the degenerate Hopf bifurcation with $O(2)$ symmetry by E. Knobloch Doubly diffusive waves by E. Knobloch, A. E. Deane, J. Toomre, and D. R. Moore An example of symmetry breaking with submaximal isotropy subgroup by R. Lauterbach A codimension-three bifurcation arising in Langmuir circulations by I. Moroz Symmetric Hopf bifurcations and magnetoconvection by W. Nagata Columnar convection in double-diffusive systems by M. R. E. Proctor Codimension two bifurcation in a convection experiment by I. Rehberg and G. Ahlers The Hopf bifurcation on a hexagonal lattice by M. Roberts, J. Swift, and D. Wagner Completely integrable Hamiltonian systems on semi-simple Lie algebras by D. H. Sattinger Bifurcation without mixed mode solutions by L. Turyn Hopf bifurcation at non-semisimple eigenvalues by A. Vanderbauwhede Abstracts: Interaction of azimuthal modes in the Couette-Taylor problem by P. Chossat Slowly varying bifurcation parameters by T. Erneux and E. L. Reiss Applications of singularity theory to explosion theory by B. F. Gray Externally modulated convection: theory and experiment by P. C. Hohenberg, G. Ahlers, and M. Lucke Equivariant normal forms for the Taylor-Couette problem by W. F. Langford Development of spatial and temporal complexity in Langmuir circulation by S. Leibovich, S. K. Lele, and I. M. Moroz Steady-state multiplicity features of chemically reacting systems by D. Luss Bibliographical notes on generic bifurcations in Hamiltonian systems by K. R. Meyer Multicritical points in flow between independently rotating cylinders by R. Tagg.
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