Ian Melbourne's Publication List

Publications 1986-2000

  1. I. Melbourne. Validity, universality and structure of the Ginzburg-Landau equation. Equadiff 99, International Conference on Differential Equations , (B. Fiedler et al. eds.) World Scientific, Singapore, 2000, 186-200
    ( abstract, pdf file )

  2. I. Melbourne. Ginzburg-Landau theory and symmetry. Review article. In: Nonlinear Instability, Chaos and Turbulence, Vol 2 , (L. Debnath and D. N. Riahi, eds.) Advances in Fluid Mechanics 25 WIT Press, Southampton, 2000, 79-109
    ( abstract, pdf file )

  3. J. S. W. Lamb, I. Melbourne and C. Wulff. Bifurcation from periodic and relative periodic solutions in equivariant dynamical systems. Equadiff 99, International Conference on Differential Equations , (B. Fiedler et al. eds.) World Scientific, Singapore, 2000, 175-185
    ( abstract, pdf file )

  4. I. Melbourne. Hidden symmetries on partially unbounded domains. Physica D 143 (2000) 226-234
    ( abstract, pdf file )

  5. M. Golubitsky, V. G. LeBlanc and I. Melbourne. Hopf bifurcation from rotating waves and patterns in physical space. J. Nonlin. Sci 10 (2000) 69-101
    ( abstract, pdf file )

  6. P. Ashwin, I. Melbourne and M. Nicol. Drift bifurcations of relative equilibria and transitions of spiral waves. Nonlinearity 12 (1999) 741-755
    ( abstract, pdf file )

  7. J. S. W. Lamb and I. Melbourne. Bifurcation from discrete rotating waves. Arch. Rat. Mech. Anal. 149 (1999) 229-270
    ( abstract, pdf file )

  8. J. S. W. Lamb and I. Melbourne. Bifurcation from periodic solutions with spatiotemporal symmetry. Pattern Formation in Continuous and Coupled Systems (M. Golubitsky, D. Luss and S. Strogatz, eds). IMA Volumes in Mathematics and its Applications 115, Springer, 1999, 175-191
    ( abstract, pdf file )

  9. P. Chossat, M. Krupa, I. Melbourne and A. Scheel. Magnetic dynamos in rotating convection --- A dynamical systems approach. Dynamics of Continuous, Discrete and Impulsive Systems 5 (1999) 327-340
    ( abstract, pdf file )

  10. I. Melbourne. Steady-state bifurcation with Euclidean symmetry. Trans. Amer. Math. Soc. 351 (1999) 1575-1603
    ( abstract, pdf file )

  11. I. Melbourne. Derivation of the time-dependent Ginzburg-Landau equation on the line. J. Nonlin. Sci. 8 (1998) 1-15
    ( abstract, pdf file )

  12. P. Chossat, M. Krupa, I. Melbourne and A. Scheel. Transverse bifurcations of heteroclinic cycles in symmetric systems. Physica D 100 (1997) 85-100
    ( abstract , pdf file )

  13. I. Melbourne and I. Stewart. Symmetric ω-limit sets for smooth Γ-equivariant dynamical systems with Γ0 abelian. Nonlinearity 10 (1997) 1551-1567
    ( abstract, pdf file )

  14. P. Ashwin and I. Melbourne. Noncompact drift for relative equilibria and relative periodic orbits. Nonlinearity 10 (1997) 595-616
    ( abstract, pdf file )

  15. M. Golubitsky, V. G. LeBlanc and I. Melbourne. Meandering of the spiral tip: an alternative approach. J. Nonlin. Sci. 7 (1997) 557-586
    ( abstract, pdf file )

  16. M. Field, I. Melbourne and M. Nicol. Symmetric attractors for diffeomorphisms and flows. Proc. London Math. Soc. 72 (1996) 657-696
    ( abstract, pdf file )

  17. I. Melbourne. Generalizations of a result on symmetry groups of attractors. Pattern Formation: Symmetry Methods and Applications (J. Chadam et al. eds.) Fields Institute Communications 5, Amer. Math. Soc., Providence, RI, 1996
    ( abstract / pdf file )

  18. I. Bosch Vivancos, P. Chossat and I. Melbourne. New planforms in systems of partial differential equations with Euclidean symmetry. Arch. Rat. Mech. Anal. 131 (1995) 199-224
    ( abstract, pdf file )

  19. M. Krupa and I. Melbourne. Asymptotic stability of heteroclinic cycles in systems with symmetry. Ergodic Theory Dyn. Syst. 15 (1995) 121-147
    ( abstract , pdf file )

  20. M. Krupa and I. Melbourne. Nonasymptotically stable attractors in O(2) mode interactions. Normal Forms and Homoclinic Chaos (W. Langford and W. Nagata eds.) Fields Institute Communications 4, Amer. Math. Soc., Providence, RI, 1995, 219-232
    ( abstract , pdf file )

  21. M. Dellnitz and I. Melbourne. A note on the shadowing lemma and symmetric periodic points. Nonlinearity 8 (1995) 1067-1075
    ( abstract, pdf file )

  22. P. Ashwin and I. Melbourne. Symmetry groups of attractors. Arch. Rat. Mech. Anal. 126 (1994) 59-78
    ( abstract, pdf file )

  23. I. Melbourne. Instantaneous symmetry and symmetry on average in the Couette-Taylor and Faraday experiments. Dynamics, Bifurcations, Symmetry (P. Chossat ed.) Kluwer, The Netherlands, 1994, 241-257
    ( abstract, pdf file )

  24. M. Dellnitz and I. Melbourne. Generic movement of eigenvalues for equivariant selfadjoint matrices. J. Comp. Appl. Math. 55 (1994) 249-259
    ( abstract )

  25. I. Melbourne. Maximal isotropy subgroups for absolutely irreducible representations of compact Lie groups. Nonlinearity 7 (1994) 1385-1393
    ( abstract, pdf file )

  26. I. Melbourne. Versal unfoldings of equivariant linear Hamiltonian vector fields. Math. Proc. Camb. Philos. Soc. 114 (1993) 559-573
    ( abstract, pdf file )

  27. I. Melbourne and M. Dellnitz. Normal forms for linear Hamiltonian vector fields commuting with the action of a compact Lie group. Math. Proc. Camb. Philos. Soc. 114 (1993) 235-268
    ( abstract, pdf file )

  28. M. Dellnitz and I. Melbourne. The equivariant Darboux theorem. Exploiting Symmetry in Applied and Numerical Analysis (E. Allgower et al eds.) 1992 AMS-SIAM Summer Seminar Proceedings. Lectures in Appl. Math. 29 (1993) 163-169
    ( abstract, pdf file )

  29. I. Melbourne, M. Dellnitz and M. Golubitsky. Structure of symmetric attractors. Arch. Rat. Mech. Anal. 123 (1993) 75-98
    ( abstract, pdf file )

  30. M. Dellnitz, I. Melbourne and J. Marsden. Generic bifurcation of Hamiltonian vector fields with symmetry. Nonlinearity 5 (1992) 979-996
    ( abstract, pdf file )

  31. M. Dellnitz, J. Marsden, I. Melbourne and J. Scheurle. Generic bifurcations of pendula. Bifurcation and Symmetry (E. Allgower et al eds.) ISNM 104, Birkhauser, Basel, 1992, 111-122

  32. M. Dellnitz, M. Golubitsky and I. Melbourne. Mechanisms of symmetry creation. Bifurcation and Symmetry (E. Allgower et al. eds.) ISNM 104, Birkhauser, Basel, 1992, 99-109
    ( abstract )

  33. E. Barany and I. Melbourne. A family of stable equilibria in bifurcation with spherical symmetry, SIAM J. Math. Anal. 23 (1992) 72-80
    ( abstract )

  34. I. Melbourne. An example of a non-asymptotically stable attractor, Nonlinearity 4 (1991) 835-844
    ( abstract )

  35. P. Chossat, R. Lauterbach and I. Melbourne. Steady-state bifurcation with O(3)-symmetry, Arch. Rat. Mech. Anal. 113 (1990) 313-376
    ( abstract )

  36. I. Melbourne, P. Chossat and M. Golubitsky. Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry, Proc. Roy. Soc. Edinburgh 113A (1989) 315-345. Also in New Directions in Differential Equations and Dynamical Systems J.M. Ball ed. Roy. Soc. Edinburgh (1991)
    ( abstract )

  37. I. Melbourne. Intermittency as a codimension three phenomenon, J. Dyn. Diff. Eqn. 1 (1989) 347-367
    ( abstract )

  38. I. Melbourne. The recognition problem for equivariant singularities, Nonlinearity 1 (1988) 215-240
    ( abstract )

  39. I. Melbourne. A singularity theory analysis of bifurcation problems with octahedral symmetry, Dynam. Stab. Sys. 1 (1986) 293-321
    ( abstract )