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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.

References [Enhancements On Off] (What's this?)

  • 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
American Mathematical Society