Noncompact drift for relative equilibria and relative periodic orbits

Nonlinearity

Volumn 10, Issue 3, 1997, Pages 595-616

  Ashwin, Peter ^a   Melbourne, Ian ^b  

^a UNIVERSITY OF SURREY   (United Kingdom)

^b University of Houston   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001667320     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/10/3/002     Document Type: Article

References (23)

1. Abraham R, Marsden J E and Ratiu T 1983 Manifolds, Tensor Analysis, and Applications (Reading, MA: Addison-Wesley)
2. Barkley D 1991 A model for fast computer-simulation of waves in excitable media. Physica D 49 61-70
3. Barkley D 1994 Euclidean symmetry and the dynamics of rotating spiral waves Phys. Rev. Lett. 72 165-7
4. Bredon G E 1972 Introduction to Compact Transformation Groups (Pure and Applied Mathematics 46) (New York: Academic)
5. Bröcker T and tom Dieck T 1985 Representations of Compact Lie Group (Graduate Texts in Mathematics 98) (New York: Springer)
6. Carter R W, Segal G and MacDonald I G 1995 Lectures on Lie Groups and Lie Algebras (London Mathematical Society Student Texts 32) (Cambridge: Cambridge University Press)
7. Ermakova E A, Pertsov A M and Shnol E E 1989 On the interaction of vortices in two-dimensional active media Physica D 40 185-90
8. Fiedler B, Sandstede B, Scheel A and Wulff C 1996 Bifurcation from relative equilibria of noncompact group actions: skew products, meanders and drifts Documenta Math. 1 479-505
9. Field M J 1980 Equivariant dynamical systems Trans. Am. Math. Soc. 259 185-205
10. Field M J 1991 Local structure for equivariant dynamics Singularity Theory and its Applications (Lecture Notes in Mathematics 1463) part II, ed M Roberts and I Stewart (Berlin: Springer) pp 142-66
11. Golubitsky M, LeBlanc V G and Melbourne I Meandering of the spiral tip, an alternative approach J. Nonlin. Sci. to appear
12. Henry D 1981 Geometric Theory of Semilinear Parabolic Equations (Lecture Notes in Mathematics 840) (Berlin: Springer)
13. Hunt B R, Sauer T and Yorke J A 1992 Prevalence, a translation-invariant 'almost every' on infinite-dimensional spaces, Bull. Am. Math. Soc. 27 217-38
14. Krupa M 1990 Bifurcations of relative equilibria. SIAM J. Math. Anal. 21 1453-86
15. Li G, Ouyang Q, Petrov V and Swinney H L 1996 Transition from simple rotating chemical spirals to meandering and traveling spirals Phys. Rev. Lett. 77 2105-8
16. Lojasiewicz S 1965 Ensembles Semi-Analytiques (IHES Lecture Notes)
17. Sandstede B, Scheel A and Wulff C Center-manifold reduction for spiral waves C. R. Acad. Sci. Paris to appear
18. Sandstede B, Scheel A and Wulff C Dynamics of spiral waves in unbounded domains using centre-manifold reductions Preprint
19. Varadarajan V S 1984 Lie Groups, Lie algebras, and their Representations (Graduate Texts in Mathematics 102) (New York: Springer)
20. Winfree A T 1973 Scroll-shaped waves of chemical activity in three dimensions Science 181 937-9
21. Winfree A T 1987 When Time Breaks Down (Princeton, NJ: Princeton University Press)
22. Winfree A T and Strogatz S H 1984 Organizing centres for three-dimensional chemical waves Nature 311 611-15
23. Wulff C 1996 Theory of meandering and drifting spiral waves in reaction-diffusion systems PhD Thesis Freie Universität, Berlin