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2012/11/28
10:45-11:45 Room #002 (Graduate School of Math. Sci. Bldg.)
Pascal Chossat (CNRS / University of Nice)
Pattern formation in the hyperbolic plane (ENGLISH)
Pascal Chossat (CNRS / University of Nice)
Pattern formation in the hyperbolic plane (ENGLISH)
[ Abstract ]
Initially motivated by a model for the visual perception of textures by the cortex, the problem of pattern formation in the hyperbolic plane, or equivalently the Poincaré disc D, shows some similar but mostly quite different features from the same problem posed on the Euclidean plane. The hyperbolic structure induces a large variety of possible periodic patterns and even the bifurcation of "hyperbolic" traveling waves. We call these patterns "H-planforms". I shall show how H-planforms are determined by the means of equivariant bifurcation theory and Helgason-Fourier analysis in D. However the question of their observability is still open. The talk will be illustrated with pictures of H-planforms that have been computed using non trivial algorithms based on harmonic analysis in D.
Initially motivated by a model for the visual perception of textures by the cortex, the problem of pattern formation in the hyperbolic plane, or equivalently the Poincaré disc D, shows some similar but mostly quite different features from the same problem posed on the Euclidean plane. The hyperbolic structure induces a large variety of possible periodic patterns and even the bifurcation of "hyperbolic" traveling waves. We call these patterns "H-planforms". I shall show how H-planforms are determined by the means of equivariant bifurcation theory and Helgason-Fourier analysis in D. However the question of their observability is still open. The talk will be illustrated with pictures of H-planforms that have been computed using non trivial algorithms based on harmonic analysis in D.
