Author | Arnol'd, V. I. author |
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Title | Huygens and Barrow, Newton and Hooke [electronic resource] : Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals / by V. I. Arnol'd |
Imprint | Basel : Birkhรคuser Basel, 1990 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-9129-5 |
Descript | 118 p. 1 illus. online resource |
Huygens and Barrow, Newton and Hooke -- 1. The law of universal gravitation -- ยง 1. Newton and Hooke -- ยง 2. The problem of falling bodies -- ยง 3. The inverse square law -- ยง 4. The Principia -- ยง 5. Attraction of spheres -- ยง 6. Did Newton prove that orbits are elliptic? -- 2. Mathematical analysis -- ยง 7. Analysis by means of power series -- ยง 8. The Newton polygon -- ยง 9. Barrow -- ยง10. Taylor series -- ยง11. Leibniz -- ยง12. Discussion on the invention of analysis -- 3. From evolvents to quasicrystals -- ยง13. The evolvents of Huygens -- ยง14. The wave fronts of Huygens -- ยง15. Evolvents and the icosahedron -- ยง16. The icosahedron and quasicrystals -- 4. Celestial mechanics -- ยง17. Newton after the Principia -- ยง18. The natural philosophy of Newton -- ยง19. The triumphs of celestial mechanics -- ยง20. Laplace's theorem on stability -- ยง21. Will the Moon fall to Earth? -- ยง22. The three body problem -- ยง23. The Titius-Bode law and the minor planets -- ยง24. Gaps and resonances -- 5. Kepler's second law and the topology of Abelian integrals -- ยง25. Newton's theorem on the transcendence of integrals -- ยง26. Local and global algebraicity -- ยง27. Newton's theorem on local non-algebraicity -- ยง28. Analyticity of smooth algebraic curves -- ยง29. Algebraicity of locally algebraically integrable ovals -- ยง30. Algebraically non-integrable curves with singularities -- ยง31. Newton's proof and modern mathematics -- Appendix 1. Proof that orbits are elliptic -- Appendix 2. Lemma XXVIII of Newton's Principia -- Notes