Bulletin (New Series) of the American Mathematical Society

Hopf bifurcation in the presence of symmetry

Martin Golubitsky and Ian Stewart

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc. (N.S.) Volume 11, Number 2 (1984), 339-342.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
http://projecteuclid.org/euclid.bams/1183552172

Mathematical Reviews number (MathSciNet)
MR752793

Zentralblatt MATH identifier
0554.58045

Subjects
Primary: 58F22
Secondary: 58F14

Citation

Golubitsky, Martin; Stewart, Ian. Hopf bifurcation in the presence of symmetry. Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 2, 339--342. http://projecteuclid.org/euclid.bams/1183552172.


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References

  • J. Alexander and J. F. G. Auchmuty [1984], Bifurcation of phase-locked solutions of coupled oscillators (in preparation).
  • J. F. G. Auchmuty [1979], Bifurcating waves, Ann. New York Acad. Sci. 316, 263-278.
  • A. K. Bajaj [1982], Bifurcating periodic solutions in rotationally symmetric systems, SIAM J. Appl. Math. 42, 1078-1098.
  • P. Chossat and G. Iooss [1984], Primary and secondary bifurcation in the Couette-Taylor problem, Nice (preprint).
  • S. N. Chow, J. Mallet-Paret and J. Yorke [1978], Global Hopf bifurcation from a multiple eigenvalue, Nonlinear Anal. 2, 753-763.
  • G. Cicogna [1981], Symmetry breakdown for bifurcations, Lett. Nuovo. Cimento (2) 31, 600-602.
  • M. Golubitsky and W. F. Langford [1981], Classification and unfoldings of degenerate Hopf bifurcations, J. Differential Equations 41, 375-415.
  • M. Golubitsky and I. N. Stewart [1984a], Hopf bifurcation in the presence of symmetry, Arch. Rational Mech. Anal. (to appear).
  • M. Golubitsky and I. N. Stewart [1984b], Symmetry and stability in Taylor-Couette flow, SIAM J. Math. Anal. (submitted).
  • J. K. Hale [1978], Nonlinear analysis and mechanics: Heriot-Watt Symposium, Vol. I (R. J. Knopf, ed.), Res. Notes in Math., Vol. 17, Pitman, San Francisco, pp. 59-157.
  • E. Ihrig and M. Golubitsky [1984], Pattern selection with O (3) symmetry, Phys. D (to appear).
  • H. Kielhöfer and R. Lauterbach [1983], On the principle of reduced stability, J. Funct. Anal. 53, 99-111.
  • J. E. Marsden and M. McCracken [1976], The Hopf bifurcation and its applications, Appl. Math. Sci. 19, Springer, New York.
  • D. Rand [1982], Dynamics and symmetry: Predictions for modulated waves in rotating fluids, Arch. Rational Mech. Anal. 79, 1-38.
  • M. Renardy [1982], Bifurcation from rotating waves, Arch. Rational Mech. Anal. 75, 49-84.
  • D. Ruelle [1973], Bifurcation in the presence of a symmetry group, Arch. Rational Mech. Anal. 51, 136-152.
  • D. H. Sattinger [1983], Branching in the presence of symmetry, CBMS Regional Conf. Ser. in Appl. Math., no. 40, SIAM, Philadelphia.
  • S. Schecter [1976], Bifurcations with symmetry, The Hopf bifurcation and Its Applications (J. E. Marsden and M. McCracken, eds.), Appl. Math. Sci. 19, Springer, New York, pp. 224-249.
  • S. A. Van Gils [1984], Some studies in dynamical system theory, Ph.D. Thesis, Vrije Univ., Amsterdam.