Combining stability with symmetry properties in bifurcation problems
Rendiconti del Seminario Matematico della Università di Padova, Tome 76 (1986) , pp. 137-148.
@article{RSMUP_1986__76__137_0,
author = {Cicogna, G.},
title = {Combining stability with symmetry properties in bifurcation problems},
journal = {Rendiconti del Seminario Matematico della Universit\a di Padova},
pages = {137--148},
publisher = {Seminario Matematico of the University of Padua},
volume = {76},
year = {1986},
zbl = {0612.58026},
mrnumber = {881565},
language = {en},
url = {http://www.numdam.org/item/RSMUP_1986__76__137_0/}
}
Cicogna, G. Combining stability with symmetry properties in bifurcation problems. Rendiconti del Seminario Matematico della Università di Padova, Tome 76 (1986) , pp. 137-148. http://www.numdam.org/item/RSMUP_1986__76__137_0/`

[1] S.R. Bernfeld - P. Negrini - L. Salvadori, Quasi-invariant manifolds, stability, and generalized Hopf bifurcation, Ann. Mat. Pura Appl., (IV), CXXX (1982), p. 1070. | MR 663967 | Zbl 0493.34030

[2] S.R. Bernfeld - L. Salvadori - F. Visentin: Hopf bifurcation and related stability problems for periodic differential systems, to be published. | Zbl 0595.34048

[3] G. Cicogna, Symmetry breakdown from bifurcation, Lett. Nuovo Cim., 31 (1981), p. 600. | MR 631456

[4] G. Cicogna, Bifurcation and symmetries, Boll. Un. Mat. Ital., 1-B (1982), p. 787. | MR 666605 | Zbl 0502.58024

[5] G. Cicogna, Bifurcation from topology and symmetry arguments, Boll. Un. Mat. Ital., 3-A (1984), p. 131. | MR 739200 | Zbl 0535.58011

[6] M. Golubitsky, The Bénard problem, symmetry, and the lattice of isotropy subgroups, in: Bifurcation Theory, Mechanics and Physics (C. P. Bruter et al., ed.s), p. 225, Reidel, Dordrecht, 1983. | MR 726253 | Zbl 0542.76054

[7] M. Golubitsky - E. Ihrig, Pattern selection with O3 symmetry, Physica, 13D (1984), p. 1. | MR 775276 | Zbl 0581.22021

[8] M. Golubitsky - I. Stewart, Hopf bifurcation in the presence of symmetry, Arch. Rat. Mech. Anal., 87 (1985), p. 107. | MR 765596 | Zbl 0588.34030

[9] G. Iooss - D.D. Joseph, Elementary Stability and Bifurcation Theory, U.T.M., Springer-Verlag, New York, 1980. | MR 636256 | Zbl 0691.34002

[10] L. Michel, Nonlinear group action. Smooth action of compact Lie groups on manifolds, in: Statistical Mechanics and Field Theory (R. N. Sen, C. Weil ed.s), p. 133, Israel Univ. Press, Jerusalem, 1972. | Zbl 0255.57019

[11] L. Michel, Symmetry defects and broken symmetry, Rev. Mod. Phys., 52 (1980), p. 617. | MR 578143

[12] P. Negrini - L. Salvadori, Attractivity and Hopf bifurcation, Nonlin. Anal., T.M.A., 3 (1979), p. 87. | MR 520476 | Zbl 0423.34062

[13] L. Salvadori, An approach to bifurcation via stability theory, Proc. of the Conf. on Recent Advances in Nonlinear Analysis and Differential Equations, Madras, 1981.

[14] L. Salvadori, Exchange of stability and bifurcation for periodic differential systems, Proc. of VI Int. Conf. on Trends in Theory and Practice of Nonlinear Analysis, North-Holland Elsevier (in printing). | MR 817517 | Zbl 0577.34044

[15] L. Salvadori, Lectures notes at the 9th Summer School of Mathematical Physics (Ravello, 1984), and at the Meeting on Nonlinear Oscillations o Conservative Systems (Venezia, 1985).

[16] D.H. Sattinger, Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics n. 309, Springer-verlag, Berlin, 1972. | MR 463624 | Zbl 0248.35003

[17] D.H. Sattinger, Group Theoretic Methods in Bifurcation Theory, Lecture Notes in Mathematics n. 762, Springer-Verlag, Berlin, 1979. | MR 551626 | Zbl 0414.58013

[18] D.H. Sattinger, Branching in the Presence of Symmetry, CBMS-NSF, Reg. Conf. on Appl. Math., SIAM, Philadelphia, 1983. | MR 764932 | Zbl 0516.58016

[19] A. Vanderbauwhede, An abstract setting for the study of the Hopf bifurcation, Nonlin. Anal., T.M.A., 4 (1980), p. 547. | MR 574372 | Zbl 0437.47044

[20] A. Vanderbauwhede, Local Bifurcation and Symmetry, Pitman Research Notes in Mathematics, vol. 75, Boston, 1982. | MR 697724 | Zbl 0539.58022

[21] A. Vanderbauwhede, Stability of bifurcating equilibria and the principle of reduced stability, pp. 209-223, in: Bifurcation Theory and Applications CIME Lect. Notes, Montecatini 1983 (ed. L. Salvadori), Lecture Notes in Mathematics n. 1057, Springer-Verlag, Berlin, 1984. | MR 753302 | Zbl 0541.58038