Open Access
Translator Disclaimer
1996 Hopf bifurcation on the hexagonal lattice with small frequency
Michael Renardy
Adv. Differential Equations 1(2): 283-299 (1996).


Hopf bifurcations with symmetry are typically treated in a two-step process: First the center manifold theorem is used to reduce the equations to a finite dimensional system, and then the resulting ordinary differential equations are reduced to Birkhoff normal form. The latter step involves transformations where the frequency appears in the denominator. In this paper, we are interested in situations where the frequency at the bifurcation point is small, and it would be of interest to consider bifurcated solutions with amplitudes on the same order as the frequency. In this case, the Birkhoff normal form breaks down, and the bifurcation equations become significantly more complex. We consider the Hopf bifurcation on the hexagonal lattice in this context. A possible application arises in the two-layer Bénard problem.


Download Citation

Michael Renardy. "Hopf bifurcation on the hexagonal lattice with small frequency." Adv. Differential Equations 1 (2) 283 - 299, 1996.


Published: 1996
First available in Project Euclid: 25 April 2013

zbMATH: 0844.34030
MathSciNet: MR1364005

Primary: 34C23
Secondary: 58F14 , 76E15

Rights: Copyright © 1996 Khayyam Publishing, Inc.


Vol.1 • No. 2 • 1996
Back to Top