Huygens and Barrow, Newton and Hooke: Pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals

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Springer Science & Business Media, 1 de jul. 1990 - 118 pàgines

Translated from the Russian by E.J.F. Primrose
"Remarkable little book." -SIAM REVIEW
V.I. Arnold, who is renowned for his lively style, retraces the beginnings of mathematical analysis and theoretical physics in the works (and the intrigues!) of the great scientists of the 17th century.
Some of Huygens' and Newton's ideas. several centuries ahead of their time, were developed only recently. The author follows the link between their inception and the breakthroughs in contemporary mathematics and physics.
The book provides present-day generalizations of Newton's theorems on the elliptical shape of orbits and on the transcendence of abelian integrals; it offers a brief review of the theory of regular and chaotic movement in celestial mechanics, including the problem of ports in the distribution of smaller planets and a discussion of the structure of planetary rings.

 

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Continguts

Huygens and Barrow Newton and Hooke
Chapter 2
12 Discussion on the invention of analysis
15 Evolvents and the icosahedron
15
Indications bibliographiques sur le Chapitre I
58
JL Verdier Dualité dans la cohomologie des groupes profinis
64
Généralités
82
Corps de dimension s 1
88
Corps de nombres algébriques
115
Annexe Cohomologie galoisienne des extensions transcendantes pures
120
Formes
128
Corps de dimension s 1
135
Corps de dimension s 2
146
Indications bibliographiques sur le Chapitre III
161
Bibliographie
171
Copyright

Corps padiques
100

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