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We judge symplectic integrators by the accuracy with which they represent the Hamil-tonian function. This accuracy is computed, compared and tested for several diierent methods. We develop new, highly accurate explicit fourth-and fth-order methods valid when the Hamiltonian is separable with quadratic kinetic energy. For the near-integrable case, we connrm… (More)

- Pau Atela, Christophe Golé
- 2000

- 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
- 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 mech-anistically relevant representation of a pattern. The ontogenetic graph is extracted from the local geometry of the… (More)

It has been known since Julia that polynomials commuting under composition have the same Julia set. More recently in the works of Baker and Eremenko, Fernández, and Beardon, results were given on the converse question: When do two polynomials have the same Julia set? We give a complete answer to this question and show the exact relation between the two… (More)

- 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

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