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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)
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)
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)
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