Christophe Golé

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We present a rigorous mathematical analysis of a discrete dynamical system modeling plant pattern formation. In this model, based on the work of physicists Douady and Couder, fixed points are the spiral or he-lical lattices often occurring in plants. The frequent occurrence of the Fibonacci sequence in the number of visible spirals is explained by the(More)
This article presents new methods for the geometrical analysis of phyllotactic patterns and their comparison with patterns produced by simple, discrete dynamical systems. We introduce the concept of ontogenetic graph as a parsimonious and mechanistically relevant representation of a pattern. The ontogenetic graph is extracted from the local geometry of the(More)
This paper gives two results that show that the dynamics of a time-periodic Lagrangian system on a hyperbolic manifold are at least as complicated as the geodesic flow of a hyperbolic metric. Given a hyperbolic geodesic in the Poincaré ball, Theorem A asserts that there are minimizers of the lift of the Lagrangian system that are a bounded distance away and(More)
This paper concentrates on optical Hamiltonian systems of T * T n , i.e. those for which H pp is a positive definite matrix, and their relationship with symplectic twist maps. We present theorems of decomposition by symplectic twist maps and existence of periodic orbits for these systems. The novelty of these results resides in the fact that no explicit(More)
Radial glia serve as the resident neural stem cells in the embryonic vertebrate nervous system, and their proliferation must be tightly regulated to generate the correct number of neuronal and glial cell progeny in the neural tube. During a forward genetic screen, we recently identified a zebrafish mutant in the kif11 loci that displayed a significant(More)