@article{upm6088,
          volume = {6},
          number = {6},
           month = {Noviembre},
          author = {Juan S{\'a}nchez and Marta Net and Jos{\'e} Manuel Vega de Prada},
           title = {Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2) equivariant systems},
       publisher = {American Institute of Mathematical Sciences (AIMS)},
            year = {2006},
         journal = {Discrete and Continuous Dynamical Systems Series B},
           pages = {1--24},
        keywords = {Amplitude equations, symmetric periodic orbits, thermal convection.},
             url = {http://oa.upm.es/6088/},
        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-Poincar{\'e} 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.}
}