Ian Melbourne's Reprint List
Bifurcation from Symmetric Periodic Solutions
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D. Chan and I. Melbourne.
A geometric characterisation of resonance in Hopf bifurcation from relative
equilibria.
Physica D 234 (2007) 98-104
( abstract,
postscript file or
pdf file )
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J. S. W. Lamb and I. Melbourne.
Normal form theory for relative equilibria and relative periodic solutions.
Trans. Amer. Math. Soc. 359 (2007) 4537-4556
( abstract,
postscript file or
pdf file )
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J. S. W. Lamb, I. Melbourne and C. Wulff.
Hopf bifurcation from relative periodic solutions;
Secondary bifurcations from meandering spirals.
J. Difference Equ. Appl. 12 (2006) 1127-1145
( abstract,
postscript file or
pdf file )
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J. S. W. Lamb, I. Melbourne and C. Wulff.
Bifurcation from periodic solutions with spatiotemporal symmetry,
including resonances and mode interactions.
J. Diff. Eq. 191 (2003) 377-407
( abstract,
postscript file or
pdf file )
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C. Wulff, J. S. W. Lamb and I. Melbourne.
Bifurcation from relative periodic solutions.
Ergodic Theory and Dynamical Systems.
21 (2001) 605-635
( abstract,
postscript file or
pdf file )
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J. S. W. Lamb and I. Melbourne.
Bifurcation from discrete rotating waves.
Arch. Rat. Mech. Anal. 149 (1999) 229-270
( abstract,
postscript file or
pdf file )
Proceedings articles
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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,
postscript file or
pdf file )
Summarizes articles 5 and 6 above, and announces new results from work
in progress
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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,
postscript file or
pdf file )
Nontechnical account of the results in article 6 above