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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

Juan Sánchez 1, , Marta Net 1, and  José M. Vega 2,

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.
Keywords: Amplitude equations, symmetric periodic orbits, thermal convection..
Mathematics Subject Classification: Primary: 37M20, 65P30; Secondary: 76D05, 76E0.
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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