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

Sánchez, Juan and Net, Marta and Vega de Prada, José Manuel (2006). Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2) equivariant systems. "Discrete and Continuous Dynamical Systems Series B", v. 6 (n. 6); pp. 1-24. ISSN 1531-3492. https://doi.org/10.3934/dcdsb.2006.6.1357.

Description

Title: Amplitude equations close to a triple-(+1) bifurcation point of D4-symmetric periodic orbits in O(2) equivariant systems
Author/s:
  • Sánchez, Juan
  • Net, Marta
  • Vega de Prada, José Manuel
Item Type: Article
Título de Revista/Publicación: Discrete and Continuous Dynamical Systems Series B
Date: November 2006
ISSN: 1531-3492
Volume: 6
Subjects:
Freetext Keywords: Amplitude equations, symmetric periodic orbits, thermal convection.
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Fundamentos Matemáticos de la Tecnología Aeronáutica [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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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.

More information

Item ID: 6088
DC Identifier: http://oa.upm.es/6088/
OAI Identifier: oai:oa.upm.es:6088
DOI: 10.3934/dcdsb.2006.6.1357
Official URL: http://aimsciences.org/journals/displayArticles.jsp?paperID=1950
Deposited by: Memoria de Investigacion 2
Deposited on: 18 Feb 2011 12:33
Last Modified: 20 Apr 2016 14:43
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