American Institute of Mathematical Sciences

November  2006, 6(6): 1357-1380. doi: 10.3934/dcdsb.2006.6.1357

Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2)-equivariant systems

 1 Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n. Campus Nord. Mòdul B4, 08034 Barcelona, Spain, Spain 2 E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Pl. Cardenal Cisneros 3, 28040 Madrid, Spain

Received  July 2005 Revised  June 2006 Published  August 2006

A two-dimensional thermal convection problem in a circular annulus subject to a constant inward radial gravity and heated from the inside is considered. A branch of spatio-temporal symmetric periodic orbits that are known only numerically shows a multi-critical codimension-two point with a triple +1-Floquet multiplier. The weakly nonlinear analysis of the dynamics near such point is performed by deriving a system of amplitude equations using a perturbation technique, which is an extension of the Lindstedt-Poincaré method, and solvability conditions. The results obtained using the amplitude equation are compared with those from the original system of partial differential equations showing a very good agreement.
Citation: Juan Sánchez, Marta Net, José M. Vega. Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2)-equivariant systems. Discrete & Continuous Dynamical Systems - B, 2006, 6 (6) : 1357-1380. doi: 10.3934/dcdsb.2006.6.1357
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