Η ΕΠΙΣΤΗΜΗ ΤΟΥ ΧΑΟΥΣ
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Transcript of Η ΕΠΙΣΤΗΜΗ ΤΟΥ ΧΑΟΥΣ
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H EITHMH TOY XAOY
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pi
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James A. Yorke.
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pi : f(x) = ax + b
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pi pi..
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pi .
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pi :
f(x) = 2x + 1 = f(x)
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= 1, f(1) = 2.1 + 1 = 2pi pi pi pi
= 2, f(2) = 2.2 + 1 = 5 .
, pi
pi .
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pi pi pi pi pi pi
:
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f(x) = x2 + c x = f(x) pi c pi
pi pi
pi pi.
c = 0 c = 0
pi .(
"" ).
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> 1 pi
pi :
f(2)=4
f(4)=8f(4)=8
f(8)=64
...
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= 1 pi
1 :
f(1)=1
f(1)=1f(1)=1
...
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< 1 pi
:
f(1/2)=1/4
f(1/4)=1/8f(1/4)=1/8
f(1/8)=1/64
...
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To pi
1 pi.
pi pipi
pi
"" pi, "" pi,
pi pi pi
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pi .
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c pi
pi
.
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Professor Ian Stewart, Mathematics Institute, University of
Warwick, Chaos and complexity, Concepts I, Sensitivity to
Initial Conditions, Euro Pace, 2000
Professor Ian Stewart, Mathematics Institute, University of
Warwick, Chaos and complexity, Concepts II, Strange
Attractors, Euro Pace, 2000
Professor Ian Stewart, Mathematics Institute, University of Professor Ian Stewart, Mathematics Institute, University of
Warwick, Chaos and complexity, Concepts I, Fractals, Euro
Pace, 2000
Benoit Mandelbrot, The Fractal Geometry of Nature, Freeman,
1982
Ian Stewart, Does God Play Dice?, Penguin, 1989
Francis C. Moon, Chaotic and Fractal Dynamics
David Ruelle, Chaotic Evolution and Strange Attractors
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:
www.alumni.imsa.edu.htm
www.en.wikipedia.org.htm
www.mathworld.wolfram.com.htm
www.people.bath.ac.uk.htm
www.universe-review.ca.htm
www.dhusara.com.htm
www.duke.edu.htm
www.ecotao.com.htm
www.hk-phy.org.htm
www.imho.com.htmwww.imho.com.htm
www.jracademy.com.htm
www.kheeper.net.htm
www.lifesmith.com.htm
www.mathjmendl.org.htm
www.mindtrap.gr.htm
www.ncbi.nml.nih.gov.htm
www.ortho.lsuhsc.edu.htm
www.physics4u.gr.com
www.win.ca.htm
www.chaos.umd.edu.htm