Amplitude equations close to a triple-(+1) bifurcation point ofD4-symmetric periodic orbits in O(2)-equivariant systems

Juan Sánchez; Marta Net; José M. Vega

doi:10.3934/dcdsb.2006.6.1357

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2006, Volume 6, Issue 6: 1357-1380. Doi: 10.3934/dcdsb.2006.6.1357

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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
2.
E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Pl. Cardenal Cisneros 3, 28040 Madrid

Received: June 30, 2005

Revised: May 31, 2006

Published: October 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 37M20, 65P30; Secondary: 76D05, 76E06.

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

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