Huygens and Barrow, Newton and Hooke: Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvents to Quasicrystals

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Springer, Jul 1, 1990 - Mathematics - 118 pages
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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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Contents

Huygens and Barrow Newton and Hooke
7
Chapter
11
The problem of falling bodies
16
The inverse square law
22
The Principle
24
Attraction of spheres
26
Did Newton prove that orbits are elliptic?
30
Chapter 2
35
Chapter 5
83
of Newtons Principia
101
Index
117
Indications bibliographiques sur le Chapitre I 58
58
JL Verdier Dualite dans la cohomologie des groupes proflnis 64
64
Generalites 82
82
Corps de dimension 1 88
88
Corps padiques 100
100

The Newton polygon
36
Barrow
38
10 Taylor series
42
11 Leibniz
44
12 Discussion on the invention of analysis
49
Chapter 3
53
14 The wave fronts of Huygens
56
15 Evolvents and the icosahedron
58
16 The icosahedron and quasicrystals
62
Celestial mechanics
67
Corps de nombres algebriques 115
115
Annexe Cohomologie galoisienne des extensions transcendantes pures
120
Formes 128
128
Corps de dimension 1
135
Corps de dimension 2
146
Indications bibliographiques sur le Chapitre III
161
Bibliographic
171
Index
180
Copyright

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JSTOR: Huygens and Barrow, Newton and Hooke: Pioneers in ...
Huygens and Barrow, Newton and Hooke: Pioneers in Mathematical Analysis and Catastrophe Theory from Evolvents to Quasicrystals. Nicholas D. Kazarinoff ...
links.jstor.org/ sici?sici=0036-1445(199109)33%3A3%3C493%3AHABNAH%3E2.0.CO%3B2-D

M.Alic: Arvet efter Hypatia; kvinnor i vetenskapens historia ...
viArnol'd: Huygens and Barrow, Newton and Hooke; pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals. ...
www.math.kth.se/ ~wannebo/ bibhem/ N-hist-A-K-01.html

Phys. Rev. E 47, R3811 (1993): Lowenstein - Quasiperiodic ...
Quasiperiodic structure of the stochastic web map. jh Lowenstein; Department of Physics, New York University, New York, New York 10003 ...
link.aps.org/ doi/ 10.1103/ PhysRevE.47.R3811

Huygens and Barrow, Newton and Hooke : - / 1990 - Livros
ARNOL'D, VI Huygens and Barrow, Newton and Hooke : pioneers in mathematical analysis and catastrophe theory from evolvents to quasicrystals .
volterra.impa.br/ arquivos/ 5000/ 7800/ 105_7829.htm

Marmi: Chaotic behaviour in the solar system
Recherche et téléchargement d’archives de revues mathématiques numérisées. Accueil · Collections · Rechercher un article · A propos · Boîte à outils ...
www.numdam.org/ numdam-bin/ fitem?id=SB_1998-1999__41__113_0

About the author (1990)

Arnol'd, Steklov Mathematical Institute

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