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The Scientific Legacy of Poincaré
About this Title
Éric Charpentier, Université Bordeaux 1, Talence, France, Étienne Ghys, École Normale Supérieure de Lyon, Lyon, France and Annick Lesne, Université Pierre et Marie Curie, Paris, France, Editors. Translated by Joshua Bowman
Publication: History of Mathematics
Publication Year:
2010; Volume 36
ISBNs: 978-0-8218-4718-3 (print); 978-1-4704-1807-6 (online)
DOI: https://doi.org/10.1090/hmath/036
MathSciNet review: MR2605614
MSC: Primary 00B15; Secondary 01A60, 30-06, 37-06, 53-06
Table of Contents
Front/Back Matter
Chapters
- Introduction
- Poincaré and his disk
- Differential equations with algebraic coefficients over arithmetic manifolds
- Poincaré and analytic number theory
- The theory of limit cycles
- Singular points of differential equations: On a theorem of Poincaré
- Periodic orbits of the three body problem: Early history, contributions of Hill and Poincaré, and some recent developments
- On the existence of closed geodesics
- Poincaré’s memoir for the Prize of King Oscar II: Celestial harmony entangled in homoclinic intersections
- Variations on Poincaré’s recurrence theorem
- Low-dimensional chaos and asymptotic time behavior in the mechanics of fluids
- The concept of “residue" after Poincaré: Cutting across all of mathematics
- The proof of the Poincaré conjecture, according to Perelman
- Henri Poincaré and the partial differential equations of mathematical physics
- Poincaré’s calculus of probabilities
- Poincaré and geometric probability
- Poincaré and Lie’s third theorem
- The Poincaré group
- Henri Poincaré as an applied mathematician
- Henri Poincaré and his thoughts on the philosophy of science