Titlebook: Bifurcation, Symmetry and Patterns; Jorge Buescu,Sofia B. S. D. Castro,Isabel Salgado Book 2003 Springer Basel AG 2003 Hot Spot.Mathemati

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Secondary Instabilities of Hexagons: A Bifurcation Analysis of Experimentally Observed Faraday Wave to three different superlattice patterns. We analyse the bifurcations involved in creating the three new patterns using a symmetry-based approach. Each of the three examples reveals a different situation that can arise in the theoretical analysis

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Piecewise Rotations: Bifurcations, Attractors and Symmetries rotations. We illustrate a new example of an attractor. The structure of this attractor appears to be present in the invertible piecewise rotation systems with two atoms. In the non-invertible case, we also illustrate a bifurcation mechanism leading to births of satellite systems.

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Pattern Formation with Galilean Symmetryon. This is because the Galilean symmetry leads to a large-scale neutral mode that interacts with the pattern. The resulting coupled amplitude equations, derived by considering the symmetry, show chaotic behaviour and exhibit a novel scaling in which the amplitude of the pattern is proportional to the 3/4 power of the bifurcation parameter.

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https://doi.org/10.1007/978-3-642-57540-2to three different superlattice patterns. We analyse the bifurcations involved in creating the three new patterns using a symmetry-based approach. Each of the three examples reveals a different situation that can arise in the theoretical analysis