Bifurcations at the dawn of Modern Science

Pierre Coullet

doi:10.1016/j.crme.2012.10.026

Bifurcations at the dawn of Modern Science

Pierre Coullet ¹

¹ INLN, UMR 7335 CNRS – Université de Nice Sophia-Antipolis, 1361 routes des Lucioles, Sophia-Antipolis, 06560 Valbonne, France

Comptes Rendus. Mécanique, Out of Equilibrium Dynamics, Volume 340 (2012) no. 11-12, pp. 777-788.

Abstract

In this article we review two classical bifurcation problems: the instability of an axisymmetric floating body studied by Archimedes, 2300 years ago and the multiplicity of images observed in curved mirrors, a problem which has been solved by Alhazen in the 11th century. We will first introduce these problems in trying to keep some of the flavor of the original analysis and then, we will show how they can be reduced to a question of extremal distances studied by Apollonius.

Published online: 2012-11-01

DOI: 10.1016/j.crme.2012.10.026

Keywords: Bifurcations, Singularities, Curved mirrors, Hydrostatics

Author's affiliations:

Pierre Coullet ¹

¹ INLN, UMR 7335 CNRS – Université de Nice Sophia-Antipolis, 1361 routes des Lucioles, Sophia-Antipolis, 06560 Valbonne, France

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Pierre Coullet. Bifurcations at the dawn of Modern Science. Comptes Rendus. Mécanique, Out of Equilibrium Dynamics, Volume 340 (2012) no. 11-12, pp. 777-788. doi : 10.1016/j.crme.2012.10.026. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.026/

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