|
Hopf bifurcation in the presence of symmetry
Authors:
Martin Golubitsky and Ian Stewart
Journal:
Bull. Amer. Math. Soc. 11 (1984), 339-342
MSC (1980):
Primary 58F22; Secondary 58F14
MathSciNet review:
752793
Full-text PDF
References |
Similar Articles |
Additional Information
-
J. Alexander and J. F. G. Auchmuty [1984], Bifurcation of phase-locked solutions of coupled oscillators (in preparation).
-
J.
F. G. Auchmuty, Bifurcating waves, Bifurcation theory and
applications in scientific disciplines (Papers, Conf., New York, 1977),
Ann. New York Acad. Sci., vol. 316, New York Acad. Sci., New York,
1979, pp. 263–278. MR 556835
(81g:35004)
-
A.
K. Bajaj, Bifurcating periodic solutions in rotationally symmetric
systems, SIAM J. Appl. Math. 42 (1982), no. 5,
1078–1098. MR 673527
(84e:58045), http://dx.doi.org/10.1137/0142075
-
P.
Chossat and G.
Iooss, Primary and secondary bifurcations in the Couette-Taylor
problem, Japan J. Appl. Math. 2 (1985), no. 1,
37–68. MR
839319 (87m:58117), http://dx.doi.org/10.1007/BF03167038
-
Shui
Nee Chow, John
Mallet-Paret, and James
A. Yorke, Global Hopf bifurcation from a multiple eigenvalue,
Nonlinear Anal. 2 (1978), no. 6, 753–763. MR 512165
(80a:58015), http://dx.doi.org/10.1016/0362-546X(78)90017-2
-
G.
Cicogna, Symmetry breakdown from bifurcation, Lett. Nuovo
Cimento (2) 31 (1981), no. 17, 600–602. MR 631456
(83f:58028)
-
Martin
Golubitsky and William
F. Langford, Classification and unfoldings of degenerate Hopf
bifurcations, J. Differential Equations 41 (1981),
no. 3, 375–415. MR 633825
(83b:58058), http://dx.doi.org/10.1016/0022-0396(81)90045-0
-
Martin
Golubitsky and Ian
Stewart, Hopf bifurcation in the presence of symmetry, Arch.
Rational Mech. Anal. 87 (1985), no. 2, 107–165.
MR 765596
(86g:58034), http://dx.doi.org/10.1007/BF00280698
-
Martin
Golubitsky and Ian
Stewart, Symmetry and stability in Taylor-Couette flow, SIAM
J. Math. Anal. 17 (1986), no. 2, 249–288. MR 826694
(87f:58033), http://dx.doi.org/10.1137/0517023
-
J.
K. Hale, Generic bifurcation with applications, Nonlinear
analysis and mechanics: Heriot-Watt Symposium (Edinburgh, 1976), Vol. I,
Pitman, London, 1977, pp. 59–157. Res. Notes in Math., No. 17.
MR
0501048 (58 #18512)
-
E.
Ihrig and M.
Golubitsky, Pattern selection with 𝑂(3) symmetry,
Phys. D 13 (1984), no. 1-2, 1–33. MR 775276
(87a:58034), http://dx.doi.org/10.1016/0167-2789(84)90268-9
-
Hansjörg
Kielhöfer and Reiner
Lauterbach, On the principle of reduced stability, J. Funct.
Anal. 53 (1983), no. 2, 99–111. MR 722505
(85e:34070), http://dx.doi.org/10.1016/0022-1236(83)90048-4
-
J.
E. Marsden and M.
McCracken, The Hopf bifurcation and its applications,
Springer-Verlag, New York, 1976. With contributions by P. Chernoff, G.
Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O.
Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt and S.
Smale; Applied Mathematical Sciences, Vol. 19. MR 0494309
(58 #13209)
-
David
Rand, Dynamics and symmetry. Predictions for modulated waves in
rotating fluids, Arch. Rational Mech. Anal. 79
(1982), no. 1, 1–37. MR 654913
(83i:58073), http://dx.doi.org/10.1007/BF02416564
-
Michael
Renardy, Bifurcation from rotating waves, Arch. Rational Mech.
Anal. 79 (1982), no. 1, 49–84. MR 654915
(83i:58026)
-
David
Ruelle, Bifurcations in the presence of a symmetry group,
Arch. Rational Mech. Anal. 51 (1973), 136–152. MR 0348796
(50 #1291)
-
D.
H. Sattinger, Branching in the presence of symmetry, CBMS-NSF
Regional Conference Series in Applied Mathematics, vol. 40, Society
for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1983. MR 764932
(86f:58031)
-
J.
E. Marsden and M.
McCracken, The Hopf bifurcation and its applications,
Springer-Verlag, New York, 1976. With contributions by P. Chernoff, G.
Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O.
Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt and S.
Smale; Applied Mathematical Sciences, Vol. 19. MR 0494309
(58 #13209)
-
S. A. Van Gils [1984], Some studies in dynamical system theory, Ph.D. Thesis, Vrije Univ., Amsterdam.
- 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. MR 556835
- A. K. Bajaj [1982], Bifurcating periodic solutions in rotationally symmetric systems, SIAM J. Appl. Math. 42, 1078-1098. MR 673527
- P. Chossat and G. Iooss [1984], Primary and secondary bifurcation in the Couette-Taylor problem, Nice (preprint). MR 839319
- S. N. Chow, J. Mallet-Paret and J. Yorke [1978], Global Hopf bifurcation from a multiple eigenvalue, Nonlinear Anal. 2, 753-763. MR 512165
- G. Cicogna [1981], Symmetry breakdown for bifurcations, Lett. Nuovo. Cimento (2) 31, 600-602. MR 631456
- M. Golubitsky and W. F. Langford [1981], Classification and unfoldings of degenerate Hopf bifurcations, J. Differential Equations 41, 375-415. MR 633825
- M. Golubitsky and I. N. Stewart [1984a], Hopf bifurcation in the presence of symmetry, Arch. Rational Mech. Anal. (to appear). MR 765596
- M. Golubitsky and I. N. Stewart [1984b], Symmetry and stability in Taylor-Couette flow, SIAM J. Math. Anal. (submitted). MR 826694
- 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. MR 501048
- E. Ihrig and M. Golubitsky [1984], Pattern selection with O (3) symmetry, Phys. D (to appear). MR 775276
- H. Kielhöfer and R. Lauterbach [1983], On the principle of reduced stability, J. Funct. Anal. 53, 99-111. MR 722505
- J. E. Marsden and M. McCracken [1976], The Hopf bifurcation and its applications, Appl. Math. Sci. 19, Springer, New York. MR 494309
- D. Rand [1982], Dynamics and symmetry: Predictions for modulated waves in rotating fluids, Arch. Rational Mech. Anal. 79, 1-38. MR 654913
- M. Renardy [1982], Bifurcation from rotating waves, Arch. Rational Mech. Anal. 75, 49-84. MR 654915
- D. Ruelle [1973], Bifurcation in the presence of a symmetry group, Arch. Rational Mech. Anal. 51, 136-152. MR 348796
- D. H. Sattinger [1983], Branching in the presence of symmetry, CBMS Regional Conf. Ser. in Appl. Math., no. 40, SIAM, Philadelphia. MR 764932
- 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. MR 494309
- S. A. Van Gils [1984], Some studies in dynamical system theory, Ph.D. Thesis, Vrije Univ., Amsterdam.
Similar Articles
Retrieve articles in Bulletin of the American Mathematical Society
with MSC (1980):
58F22,
58F14
Retrieve articles in all journals
with MSC (1980):
58F22,
58F14
Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1984-15297-2
PII:
S 0273-0979(1984)15297-2
|
