Entry
Math: Chaos theory: History: What is chaos theory?
Nov 29th, 2003 10:54
Knud van Eeden,
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--- Knud van Eeden --- 29 November 2003 - 07:15 pm -------------------
Math: Chaos theory: History: What is chaos theory?
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The idea that many simple nonlinear deterministic systems can behave in
an apparently unpredictable and chaotic manner was first noticed by the
great French mathematician
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Henri Poincaré (1854-1912)
http://www.chaos.umd.edu/misc/poincare.html
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Other early pioneering work in the field of chaotic dynamics were found
in the mathematical literature by such luminaries as:
George Birkhoff (1884-1944)
http://www-groups.dcs.st-
and.ac.uk/~history//Mathematicians/Birkhoff.html
Mary Cartwright (1900-1998)
http://www-groups.dcs.st-
and.ac.uk/~history/Mathematicians/Cartwright.html
Andrey Kolmogorov (1903-1987)
http://www-groups.dcs.st-
and.ac.uk/~history/Mathematicians/Kolmogorov.html
Norman Levinson (1912-1975)
http://www-groups.dcs.st-
and.ac.uk/~history/Mathematicians/Levinson.html
John Littlewood (1885-1977)
http://www-groups.dcs.st-
and.ac.uk/~history/Mathematicians/Littlewood.html
Stephen Smale (1930-)
http://www-groups.dcs.st-and.ac.uk/~history///Mathematicians/Smale.html
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In spite of this, the importance of chaos was not fully appreciated
until the widespread availability of digital computers for numerical
simulations and the demonstration of chaos in various physical systems.
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This realization has broad implications for many fields of science, and
it is only within the past decade or so that the field has undergone
explosive growth.
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It is found that the ideas of chaos have been very fruitful in such
diverse disciplines as
biology
chemistry
economics
engineering
fluid mechanics
physics
just to name a few.
Chaos is a multidisciplinary science, and this is reflected in the fact
that the members of the group are affiliated with diverse departments
and institutes:
Department of Physics
Department of Mathematics
Department of Electrical Engineering
Institute for Physical Sciences and Technology (IPST)
Institute for Research in Electronics and Applied Physics (IREAP)
Institute for Systems Research (ISR)
Applied Math and Scientific Computation (AMSC)
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[Internet: source: http://www.chaos.umd.edu/]
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To get a very good start of the subject, read the book 'Chaos' of James
Gleick. It will give you the feeling.
subjects:
Mitchell Feigenbaum / butterfly effect / weather / pendulum /
horseshoe / Jupiter great red spot / wildlife population / logistic
equation / bifurcation / fractal geometry / Benoit Mandelbrot /
Bourbaki /
cotton price / strange attractor / David Ruelle / Floris Takens / Lev
Landau / turbulence / fluid flow / Kolmogorov / Murray Gell-Mann /
renormalization / helium / Albert Libchaber / dimension / information
theory / heart dynamics / second law / snowflake / loaded dice
If you have read this book, you should/will know what chaos theory is.
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Chaos theory will be a sub subject teached e.g. in universities in
mathematics and physics departments (e.g. when handling non-linear
differential equations).
A lot of work in chaos is done by people in physical sciences that deal
with fluid dynamics. Mathematics is another subject that deals with
chaos.
If you want to study chaos you are going to want to study
as much mathematics as you can. And be sure to pay very close
attention to differential equations.
On a university look for courses with chaos key words like:
(Non-linear) differential equations
Chaos
Fluid dynamics
Ordinary or partial differential equations
Stability
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Chaos = the idea that disordered systems are governed by deceptively
simple mathematical relationships.
And that chaos can swiftly arise from a neat starting point in just a
few steps, with apparently trivial differences in the initial
conditions giving totally different results.
Accidently discovered in the 60's by the meteorologist Edward Lorenz
while setting up a computer model of atmospheric behaviour, its roots
can be traced back to the early years of this century and the physicist
Henri Poincar<e'>.
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[book: source: Malpass, Brian - bluff your way in science - ravette
books - 1993 - ISBN 1-85304-594-2 - p. 60]
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Chaos is a familiar phenomenon. Its rise to prominence in the 1980's
stemmed from the realization that disorderly systems tend to be
disorderly in an ORDERED fashion, and that the underlying order within
chaotic phenomena can be revealed by a combination of mathematical
analysis and computer simulations.
Mathematically, chaos is caused by 'non-linearities' in the equations
that describe a dynamical system. Here 'non-linearity' means that
changes in the output are not necessarily proportional to changes in
the input.
[book: Cipra, Barry - what's happening in the mathematical sciences
1998-1999 - American Mathematical Society - ISBN 0-8218-0766-8 - p.
21 'a prime case of chaos']
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Internet: see also:
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Math: Chaos theory: Overview: Can you give me an overview of chaos
theory?
http://www.faqts.com/knowledge_base/view.phtml/aid/26929/fid/867
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