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


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