Forced symmetry breaking perturbations for periodic solutions

Nonlinearity

Volumn 10, Issue 1, 1997, Pages 291-310

  Guyard, F ^a   Lauterbach, R ^a  

^a WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041375090     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/1/019     Document Type: Article

References (25)

1. Bierstone E 1975 Lifting isotopies from orbit spaces Topology 14 245-52
2. Bredon G E 1972 Introduction to Compact Transformation Groups (New York: Academic)
3. Bröcker T and Tom Dieck T 1985 Representations of Compact Lie Groups (Graduate Texts in Mathematics) (New York: Springer)
4. Busse F H and Riahi N 1982 Patterns of convection in spherical shells II J. Fluid Mech. 123 283-302
5. Chillingworth D R J 1985 Bifurcation from an orbit of symmetry Singularities and Dynamical Systems ed S N Pnevmatikos (Amsterdam: North-Holland) pp 285-94
6. Chillingworth D R J Bifurcation from a manifold Singularities Theory and its Applications vol 2, ed R M Roberts and I N Stewart (Berlin: Springer) pp 22-37
7. Chossat P 1979 Bifurcation and stability of convective flows in a rotating or not rotating spherical shell SIAM J. Appl. Math. 37 624-47
8. Chossat P, Lauterbach R and Melbourne I 1990 Steady-state bifurcation with o(3)-symmetry Arch. Rat. Mech. Anal. 113 313-76
9. Chossat P nd Stewart C A 1992 Spherical symmetry-breaking bifurcations and thermal convection in the earth's mantle Chaotic Processes in the Geological Sciences ed D Yuen (Berlin: Springer) pp 11-42
10. Tom Dieck T 1987 Transformation Groups (Berlin: de Gruyter)
11. Dieudonne J 1971 Eléments d'Analyse tome II (Paris: Gauthier-Villars)
12. Field M J 1980 Equivariant dynamical systems Trans. Am. Math. Soc. 259 185-205
13. Field M J 1991 Local structure of equivariant dynamics Singularity Theory and it Applications (Lecture Notes Math. 1463) ed M Roberts and I Stewart (Berlin: Springer) pp 168-95
14. Golubitsky M and Hou C 1994 An example of symmetry breaking to heteroclinic cycles Preprint University of Houston
15. Golubitsky M and Schaeffer D G 1982 Bifurcation with O(3) symmetry including applications to the spherical bénard problem Commun. Pure Appl. Math. 35 81-111
16. Golubitsky M, Schaeffer D G and Stewart I 1988 Singularities and Groups in Bifurcation Theory (Appl. Math. Sci. II) (New York: Springer)
17. Hirsch M W, Pugh C C and Shub M 1977 Invariant Manifolds (Lecture Notes Math. 583) (Berlin: Springer)
18. Ihrig E and Golubitsky M 1984 Pattern selection with O(3) symmetry Physica D 13 1-33
19. Lauterbach R 1992 Forced Symmetry Breaking from O(3) (Bifurcation and Symmetries 104) (Basel: Birkhäuser) pp 253-62
20. Lauterbach R, Maier-Paape S and Reißner E 1994 A systematic study of heteroclinic cycles in dynamical systems with broken symmetries Preprint University of Augburgs, p 309
21. Lauterbach R and Roberts M 1992 Heteroclinic cycles in dynamical systems with broken spherical symmetry J. Diff. Eqns. 100 22-48
22. Schwarz G 1975 Smooth functions invariant under the action of a compact Lie group Topology 14 245-52
23. Schwarz G 1980 Lifting Smooth Homotopies of Orbit Spaces (Publ. Math. Inst. Hautes Etudes Sci. 51) pp 37-135
24. Steenrod N E 1951 Topology of Fibre Bundles (Princeton Mathematical Series) (Princeton, NJ: Princeton University Press)
25. Yang C T 1963 The triangulation of the orbit space of a differentiable transformation group Bull. Am. Math. Soc. 69 405-8