Bulletin of the American Mathematical Society

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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.

David H. Sattinger, Topics in stability and bifurcation theory, Lecture Notes in Mathematics, Vol. 309, Springer-Verlag, Berlin-New York, 1973. MR 0463624

Klaus Kirchgässner, Bifurcation in nonlinear hydrodynamic stability, SIAM Rev. 17 (1975), no. 4, 652–683. MR 380073, DOI 10.1137/1017072

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).

Klaus Kirchgässner and Hansjörg Kielhöfer, Stability and bifurcation in fluid dynamics, Rocky Mountain J. Math. 3 (1973), 275–318. MR 319457, DOI 10.1216/RMJ-1973-3-2-275

D. H. Sattinger, Selection mechanisms for pattern formation, Arch. Rational Mech. Anal. 66 (1977), no. 1, 31–42. MR 488129, DOI 10.1007/BF00250850

D. H. Sattinger, Group representation theory and branch points of nonlinear functional equations, SIAM J. Math. Anal. 8 (1977), no. 2, 179–201. MR 438383, DOI 10.1137/0508013

D. H. Sattinger, Bifurcation from rotationally invariant states, J. Math. Phys. 19 (1978), no. 8, 1720–1732. MR 500398, DOI 10.1063/1.523871

D. H. Sattinger, Group representation theory, bifurcation theory and pattern formation, J. Functional Analysis 28 (1978), no. 1, 58–101. MR 493378, DOI 10.1016/0022-1236(78)90080-0

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

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

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, DOI 10.1002/cpa.3160320103

Martin Golubitsky and David Schaeffer, Bifurcations with $\textrm {O}(3)$ symmetry including applications to the Bénard problem, Comm. Pure Appl. Math. 35 (1982), no. 1, 81–111. MR 637496, DOI 10.1002/cpa.3160350105

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, DOI 10.1098/rsta.1983.0018

1.

D. H. Sattinger, Topics in stability and bifurcation theory, Lecture Notes in Math., vol. 309, Springer-Verlag, Berlin and New York, 1973. MR 0463624

2.

Klaus Kirchgassner, Bifurcation theory in nonlinear hydrodynamic stability, SIAM Review 17 (1975), 652-683. MR 380073

3.

D. H. Sattinger, Bifurcation and symmetry breaking, notes presented at the NSF-CBMS Conference, Univ. of Florida, 1981. 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). MR 500398

9.

D. H. Sattinger, Group representation theory, bifurcation theory and pattern formation, J. Funct. Anal. 28(1978), 1720-1732. MR 493378

10.

George H. Knightly and D. Sather, Applications of group representations to the buckling of spherical shells, Applications of Non-linear Analysis in the Physical Sciences (H. Amann et al (eds. )), Pitman, London, 1981. MR 659693

11.

George H. Knightly and D. Sather, Regularity and symmetry properties of solutions of the John Shell equations for aspherical shell, Contemporary 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), 21-98. MR 508917

13.

M. Golubitsky and D. Schaeffer, Bifurcation with O (3) symmetry including applications to the Bénard problem, Comm. Pure Appl. Math. (to appear). MR 637496

14.

Ernesto Buzano and M. Golubitsky, Bifurcation involving the hexagonal lattice, Technical Report #56, Department of Mathematics, Arizona State University, 1981. MR 713059