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Galileo UnboundA Path Across Life, the Universe and Everything$
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David D. Nolte

Print publication date: 2018

Print ISBN-13: 9780198805847

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198805847.001.0001

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From Butterflies to Hurricanes

From Butterflies to Hurricanes

Chapter:
(p.205) Chapter 9 From Butterflies to Hurricanes
Source:
Galileo Unbound
Author(s):

David D. Nolte

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198805847.003.0009

Half a century after Poincaré first glimpsed chaos in the three-body problem, the great Russian mathematician Andrey Kolmogorov presented a sketch of a theorem that could prove that orbits are stable. In the hands of Vladimir Arnold and Jürgen Moser, this became the Kolmo–Arnol–Mos (KAM) theory of Hamiltonian chaos. This chapter shows how KAM theory fed into topology in the hands of Stephen Smale and helped launch the new field of chaos theory. Edward Lorenz discovered chaos in numerical models of atmospheric weather and discovered the eponymous strange attractor. Mathematical aspects of chaos were further developed by Mitchell Feigenbaum studying bifurcations in the logistic map that describes population dynamics.

Keywords:   history of chaos, Kolmogorov, Arnold, KAM theory, three-body problem, Smale, Lorenz, strange attractor, logistic map, Feigenbaum

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