Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions

Archive for Rational Mechanics and Analysis

Volumn 145, Issue 2, 1998, Pages 129-159

  Fiedler, Bernold ^a   Turaev, Dmitry ^b  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010050153     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002050050126     Document Type: Article

References (25)

1. P. ASHWIN & I. MELBOURNE, Noncompact drift for relative equilibria and relative periodic orbits. Nonlinearity, 10, 596-616 (1997).
2. D. BARKLEY, Euclidean symmetry and the dynamics of rotating spiral waves. Phys. Rev. Lett., 72, 164-167 (1994).
3. M. BRAUNE & H. ENGEL, Compound rotation of spiral waves in a light-sensitive Belousov-Zhabotinsky medium. Chem. Phys. Lett., 204, 257-264 (1993).
4. I. BERKE & W. PHILIPP, Trigonometric series and uniform distribution mod 1. Studia Sci. Math. Hungar., 31, 15-25 (1996).
5. L. BREIMAN, Probability. Addison Wesley, New York, 1968.
6. +87] C. ELPHICK, E. TIRAPEGUI, M. BRACHET, P. COULLET. & G. IOOSS, A simple global characerization for normal forms of singular vector fields. Physica, 29D, 95-127 (1987).
7. B. FIEDLER, Global Bifurcation of Periodic Solutions with Symmetry. Springer-Verlag, Berlin, 1988.
8. B. FIEDLER, B. SANDSTEDE, A. SCHEEL, & C. WULFF, Bifurcation from relative equilibria of noncompact group actions: Skew products, meanders, and drifts. Doc. Math., 1, 479-505 (1996).
9. M. GOLUBITSKY, V. LEBLANC, & I. MELBOURNE, Meandering of the spiral tip - an alternative approach. J. Nonlinear Sci., 7, 557-586 (1997).
10. W. JAHNKE, W. E. SKAGGS, & A. T. WINFREE, Chemical vortex dynamics in the Belousov-Zhabotinskii reaction and in the two-variable Oregonator model. J. Chem. Phys., 93, 740-749 (1989).
11. M. KRUPA, Bifurcations of relative equilibria. SIAM J. Math. Analysis, 21, 1453-1486 (1990).
12. L. KUIPERS & H. NIEDERREITER, Uniform Distribution of Sequences. Wiley-Interscience, New York, 1974.
13. A. E. H. LOVE, A Treatise on the Mathematical Theory of Elasticity. New York, 1892.
14. A. MIELKE, Hamiltonian and Lagrangian Flows on Center Manifolds, Springer-Verlag, Berlin, 1991.
15. S. C. MÜLLER, V. S. ZYKOV, Simple and complex spiral wave dynamics. Phil. Trans. Royal Soc. Lond. A, 347, 677-685 (1994).
16. S. NETTESHEIM, A. VON OERTZEN, H. H. ROTERMUND, & G. ERTL, Reaction diffusion patterns in the catalytic CO-oxidation on Pt(110) - front propagation and spiral waves. J. Chem. Phys., 98, 9977-9985 (1993).
17. I. M. OVSYANNIKOV & L. P. SHIL'NIKOV, Systems with a homoclinic curve of a multidimensional saddle-focus and spiral chaos. Math. USSR Sbornik, 2, 415-443 (1992).
18. W. PHILIPP & W. STOUT, Almost sure invariance principles for partial sums of weakly dependent random variables. Mem. Amer. Math. Soc., 2 (1975).
19. D. RAND, Dynamics and symmetry: Predictions for modulated waves in rotating fluids. Arch. Rational Mech. Anal., 79, 1-38 (1982).
20. M. RENARDY, Bifurcation from rotating waves. Arch. Rational Mech. Anal., 79, 49-84 (1982).
21. B. SANDSTEDE, A. SCHEEL, & C. WULFF, Center-manifold reduction for spiral waves. C. R. Acad. Sci., Série I, 324, 153-158 (1997).
22. B. SANDSTEDE, A. SCHEEL, & C. WULFF, Dynamics of spiral waves in unbounded domains using center-manifold reductions. J. Diff. Eqs., 141, 122-149 (1997).
23. Zs. UNGVARAI-NAGY, J. UNGVARAI, & S. C. MÜLLER, Complexity in spiral wave dynamics. Chaos, 3, 15-19 (1993).
24. A. VANDERBAUWHEDE, Centre manifolds, normal forms and elementary bifurcations. Dynamics Reported, 2, 89-169 (1989).
25. C. WULFF, Theory of meandering and drifting spiral waves in reaction-diffusion syslerns. Dissertation, Berlin, 1996.