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Corpus ID: 18007977

DYNAMICAL SYSTEMS OF SIMPLICES IN DIMENSION 2 OR 3

@article{Bourgeois2009DYNAMICALSO,
title={DYNAMICAL SYSTEMS OF SIMPLICES IN DIMENSION 2 OR 3},
author={G. Bourgeois and S. Orange},
journal={arXiv: Dynamical Systems},
year={2009}
}

Let T0 = (A 0 ··· A d) be a d-simplex, G0 its centroid, S its circumsphere, O the center of S. Let (A i) be the points where S intersects the lines (G0A i), T1 the d-simplex (A 0 ··· A d), and G1 its centroid. By iterating this construction, a dynamical system of d- simplices (Ti) with centroids (Gi) is constructed. For d = 2 or 3, we prove that the sequence (OGi)i is decreasing and tends to 0. We consider the sequences (T2i)i and (T2i+1)i; for d = 2 they converge to two equilateral triangles… Expand