Amplitude equations close to a triple-(+1) bifurcation point of double-struck D sign-symmetric periodic orbits in double-struck O sign(2)-equivariant systems

Discrete and Continuous Dynamical Systems - Series B

Volumn 6, Issue 6, 2006, Pages 1357-1380

  Sánchez, Juan ^a   Net, Marta ^a   Vega, José M ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

Author keywords

Amplitude equations; Symmetric periodic orbits; Thermal convection

Indexed keywords

EID: 33750572430     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. A. Alonso, M. Net, and E. Knobloch, On the transition to columnar convection, Phys. Fluids, 7 (1995), no. 5, 935-940.
2. P. Chossat and G. Ioos, The Couette-Taylor problem. Springer, 1994.
3. S. M. Cox, Mode interactions in Rayleigh-Bénard convection, Physica D, 95 (1996), 50-61.
4. J. D. Crawford and E. Knobloch, Symmetry and symmetry-breaking bifurcations in fluid mechanics, Ann. Rev. Fluid Mech., 23 (1991), 341-387.
5. Z. A. Daya, V. B. Deyirmenjian, S. W. Morris and J. R. de Bruyn, Annular electroconvection with shear, Phys. Rev. Lett., 80 (1998), 964-967.
6. D. Henry, Geometric theory of semilinear parabolic equations. Springer, 1989.
7. M. Ishiwatari, S-I. Takehiro, and Y-Y, Hayashi, The effects of thermal conditions on the cell sizes of two-dimensional convection, J. Fluid Mech., 281 (1994), 33-50.
8. A. S. Landsberg, and E. Knobloch, Direction-reversing traveling waves, Phys. Lett. A, 159 (1991), 17-20.
9. W. F. Langford, and D. D. Rusu, Pattern formation in annular convection, Physica A, 261 (1998), 188-203.
10. J. S. W. Lamb, k-symmetry and return maps of spacetime symmetric flows, Nonlinearity, 11 (1998), 601-629.
11. J. S. W. Lamb, I. Melbourne, and C. Wulff, Bifurcation from periodic solutions with spatiotemporal symmetry, including resonances and mode interactions, J. Differential Equations, 191 (2003), 377-407.
12. M. Net, A. Alonso, and J. Sánchez, From stationary to complex time-dependent flows in two-dimensional annular thermal convection at moderate Rayleigh numbers, Phys. Fluids, 15 (2003), no. 5, 1314-1326.
13. M. Net, and J. Sánchez, Symmetric periodic orbits and global dynamics of quasi-periodic flows in an O(2) equivariant system: Two-dimensional thermal convection. Int. J. Bifurcation and Chaos., 15 (2005), no. 12, 3953-3972.
14. D. Pino, I. Mercader, and M. Net. Thermal and inertial modes of convection in a rapidly rotating annulus, Phys. Rev. E, 61 (2000), no. 2, 1507-1517.
15. J. Porter, and M. Silber, Broken Symmetries and pattern formation in two-frequency forced Faraday waves. Phys. Rev. Lett., 89 (2002), no. 8, 084501(4).
16. A. M. Rucklidge, and M. Silber, Bifurcations of periodic orbits with spatio-temporal symmetries, Nonlinearity, 11 (1998), 1435-1455.
17. 4 symmetry near the O(2) limit, Phys. Lett. A, 284 (2001), no. 2, 99-111.
18. M. Silber, and A. C. Skeldon, Parametrically excited surface waves: Two-frequency forcing, normal form symmetries, and pattern selection. Phys. Rev. E, 59 (1999), no. 5, 5446-5455.
19. J. Sánchez, M. Net, B. García-Archilla and C. Simó, Newton-Krylov continuation of periodic orbits for Navier-Stokes flows, J. Comput. Phys., 201 (2004), 13-33.