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- Christophe Golé
- 2001

- 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 helical 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
- 1995

We show that strictly abnormal geodesics arise in graded nilpotent Lie groups. We construct such a group, for which some Carnot geodesics are strictly abnormal and, in fact, not normal in any subgroup. In the 2-step case we also prove that these geodesics are always smooth. Our main technique is based on the equations for the normal and abnormal curves,… (More)

- 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… (More)

- Christophe Golé
- 1996

This paper gives two results that show that the dynamics of a timeperiodic 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)

- 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
- 1992

This paper concentrates on optical Hamiltonian systems of T T, i.e. those for which Hpp 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)

- Christophe Golé
- Scholarpedia
- 2010

The notion of stability in Dynamical Systems refers to dynamical behavior that persists under perturbation.1 By altering the nature of the persistence and the class of perturbations one obtains various forms of stability. These various forms of stability have proved to be extremely important throughout the history of dynamics. In perhaps the best known… (More)