# 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