References

1

J.D. Crawford and E. Knobloch. Symmetry breaking bifurcations in O(2) Maps, Phys. Lett. A 128 (1988) 327-331.

2

J.D. Crawford and E. Knobloch. Classification of O(2) symmetric Hopf bifurcation: no distinguished parameter, Physica D 31 (1988) 1-48.

3

H. Riecke, J.D. Crawford and E. Knobloch. Time-modulated oscillatory convection, Phys. Rev. Lett. 61 (1988) 1942-1945.

4

J.D. Crawford and E. Knobloch. On degenerate Hopf bifurcation with broken O(2) symmetry, Nonlinearity 1 (1988) 617-652.

5

J.D. Crawford, M. Golubitsky, and W. Langford. Modulated rotating waves in O(2) mode interaction, Dynamics and Stability of Systems 3 (1988) 159-175.

6

J.D. Crawford, E. Knobloch, and H. Riecke. Competing parametric instabilities with circular symmetry, Phys. Lett. A 135 (1989) 20-24.

7

J.D. Crawford, E. Knobloch, and H. Riecke. Mode interactions and symmetry, in Proc. of the International Conference on Singular Behavior and Nonlinear Dynamics, vol. 1, S. Pnevmatikos et al. (eds), Samos, Greece, World Scientific, 1989, pp. 277-297.

8

J.D. Crawford, E. Knobloch, and H. Riecke. Period-doubling mode interactions with circular symmetry, Physica D 44 (1990) 340-396.

9

H. Riecke, J.D. Crawford and E. Knobloch. Temporal modulation of a subcritical bifurcation to travelling waves, in New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena: The Geometry of Nonequilibrium, P. Coullet and P. Huerre (eds), NATO ASI Series B 237, Plenum Press, 1991, pp. 61-64.

10

J.D. Crawford, M. Golubitsky, M.G.M. Gomes, E. Knobloch. and I. Stewart, Boundary conditions as symmetry constraints, in Singularity Theory and its Applications, Warwick 1989 Part 2, R.M. Roberts and I.N. Stewart (eds), Lecture Notes in Mathematics, Springer-Verlag, 1991, pp. 63-79.

11

J.D. Crawford. Amplitude equations on unstable manifolds: singular behavior from neutral modes, in Modern Mathematical Methods in Transport Theory (Operator Theory: Advances and Applications, vol. 51), W. Greenberg and J. Polewczak (eds), Birkhauser Verlag, 1991, pp. 97-108.

12

J.D. Crawford and E. Knobloch. Symmetry and symmetry-breaking bifurcations in fluid dynamics, Annu. Rev. Fluid Mech. 23 (1991) 341-387.

13

J.D. Crawford. Surface waves in non-square containers with square symmetry, Phys. Rev. Lett. 67 (1991) 441-444.

14

J.D. Crawford. Normal forms for driven surface waves: boundary conditions, symmetry, and genericity, Physica D 52 (1991) 429-457.

15

J.D. Crawford. Introduction to bifurcation theory, Rev. Mod. Phys. 63 (1991) 991-1037.

16

J.D. Crawford, J.P. Gollub, and David Lane. Hidden symmetries of parametrically forced waves, Nonlinearity 6 (1993) 119-164.

17

J.D. Crawford. ${D_4\dot{+} T^2}$ Mode interactions and hidden rotational symmetry, Nonlinearity 7 (1994) 697-739.

18

J.D. Crawford. Amplitude expansions for instabilities in populations of globally-coupled oscillators, J. Stat. Phys. 74 (1994) 1047-1084.

19

J.D. Crawford. Universal trapping scaling on the unstable manifold of a collisionless electrostatic mode, Phys. Rev. Lett. 73 (1994) 656-659.

20

J.D. Crawford. Amplitude equations for electrostatic waves: universal singular behavior in the limit of weak instability, Phys. Plasmas 2 (1995) 97-128.

21

J.D. Crawford. Scaling and singularities in the entrainment of globally-coupled oscillators, Phys. Rev. Lett. 74 (1995) 4341-4344.

22

J.D. Crawford. D₄-symmetric maps with hidden Euclidean symmetry, in Pattern Formation: Symmetry Methods and Applications, J. Chadam et al. (eds) Amer. Math. Soc., 1995, 93-124.

23

J.D. Crawford and A. Jayaraman. Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling, Phys. Rev. Lett. 77 (1996) 3549-3552.

24

J.D. Crawford and E. Knobloch. Amplitude equations for coupled electrostatic waves in the limit of weak instability, J. Plasma Physics 60 (1998) 159-180.

25

J.D. Crawford and A. Jayaraman. Amplitude equations for unstable electrostatic waves: multiple species. J. Math. Phys., 39 (1998) 4546.

26

J.D. Crawford and K.T.R. Davies. Phase dynamical models of globally coupled oscillators: singularities and scaling with arbitrary coupling. To appear in Physica D (1999), (preprint, patt-sol/9701006 at LANL archives).

27

J.D. Crawford and A. Jayaraman. First principles justification of the ``Single Wave Model''. Phys. Plasmas. 6 (1999) 666-673.