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- Christophe Golé
- 1994

We prove the existence of at least cl(M) periodic orbits for certain time dependant Hamiltonian systems on the cotangent bundle of an arbitrary compact manifold M. These Hamiltonians are not necessarily convex but they satisfy a certain boundary condition given by a Riemannian metric on M. We discretize the variational problem by decomposing the time 1 map… (More)

- Pau Atela, Christophe Golé, Scott Hotton
- J. Nonlinear Science
- 2008

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)

- Scott Hotton, Valerie Johnson, +4 authors Jacques Dumais
- Journal of Plant Growth Regulation
- 2006

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)

- Christophe Golé
- 1996

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)

- CHRISTOPHE GOLÉ
- 1992

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)

- Kimberly Johnson, Chelsea Moriarty, +9 authors Michael J F Barresi
- Developmental biology
- 2014

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)

- Christophe Golé
- Scholarpedia
- 2010

- Pau Atela, Christophe Gole
- 2007

We introduce and study properties of phyllotactic and rhombic tilings on the cylinder. These are discrete sets of points that generalize cylindrical lattices. Rhombic tilings appear as periodic orbits of a discrete dynamical system S that models plant pattern formation by stacking disks of equal radius on the cylinder. This system has the advantage of… (More)

- Pau Atela, Christophe Golé
- 2005