Book Review

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Book Information:

Author: D. H. Sattinger

Title: Group theoretic methods in bifurcation theory

Additional book information: Lecture Notes in Math., vol. 762, Springer-Verlag, Berlin, Heidelberg, 1979, 241 pp., $14.00.

**1.**D. H. Sattinger,*Topics in stability and bifurcation theory*, Lecture Notes in Math., vol. 309, Springer-Verlag, Berlin and New York, 1973. MR**463624****2.**Klaus Kirchgassner,*Bifurcation theory in nonlinear hydrodynamic stability*, SIAM Review 17 (1975), 652-683. MR**380073****3.**D. H. Sattinger,*Spontaneous symmetry breaking: mathematical methods, applications, and problems*, Applications of nonlinear analysis in the physical sciences (Bielefeld, 1979), Surveys Reference Works Math., vol. 6, Pitman, Boston, Mass.-London, 1981, pp. 3–23. MR**659687****4.**F. Busse,*The stability of finite amplitude cellular convection and its relation to an extremum principle*, J. Fluid Mech. 30 (1967).**5.**Klaus Kirchgassner and Hansjörg Kielhöfer,*Stability and bifurcation in fluid dynamics*. Rocky Mountain J. Math. 3 (1973), 275-318. MR**319457****6.**D. H. Sattinger,*Selection mechanisms for pattern formations*, Arch. Rational Mech. Anal. 66 (1977), 31-42. MR**488129****7.**D. H. Sattinger,*Group representation theory and branch points of nonlinear functional equations*, SIAM J. Math. Anal. 8 (1977), 179-201. MR**438383****8.**D. H. Sattinger,*Bifurcation from rotationally invariant states*, J. Math. Phys.**19**(1978), no. 8, 1720–1732. MR**500398**, https://doi.org/10.1063/1.523871**9.**D. H. Sattinger,*Group representation theory, bifurcation theory and pattern formation*, J. Funct. Anal.**28**(1978), no. 1, 58–101. MR**493378**, https://doi.org/10.1016/0022-1236(78)90080-0**10.**George H. Knightly and D. Sather,*Applications of group representations to the buckling of spherical shells*, Applications of nonlinear analysis in the physical sciences (Bielefeld, 1979), Surveys Reference Works Math., vol. 6, Pitman, Boston, Mass.-London, 1981, pp. 115–138. MR**659693****11.**George H. Knightly and D. Sather,*Regularity and symmetry properties of solutions of the John shell equations for a spherical shell*, Problems of elastic stability and vibrations (Pittsburgh, Pa., 1981), Contemp. Math., vol. 4, Amer. Math. Soc., Providence, R.I., 1981, pp. 45–59. MR**641225****12.**M. Golubitsky and D. Schaeffer,*A theory for imperfect bifurcation via singularity theory*, Comm. Pure Appl. Math.**32**(1979), no. 1, 21–98. MR**508917**, https://doi.org/10.1002/cpa.3160320103**13.**Martin Golubitsky and David Schaeffer,*Bifurcations with 𝑂(3) symmetry including applications to the Bénard problem*, Comm. Pure Appl. Math.**35**(1982), no. 1, 81–111. MR**637496**, https://doi.org/10.1002/cpa.3160350105**14.**Ernesto Buzano and Martin Golubitsky,*Bifurcation involving the hexagonal lattice*, Singularities, Part 1 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 203–210. MR**713059**

Review Information:

Reviewer: J. W. Thomas

Journal: Bull. Amer. Math. Soc.

**7**(1982), 437-439

DOI: https://doi.org/10.1090/S0273-0979-1982-15060-1