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978-3-540-27305-9
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20181203160144.0
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100301s2005 gw | s |||| 0|eng d
9783540273059
978-3-540-27305-9
10.1007/b138894
doi
ISI Library, Kolkata
QA313
PBWR
bicssc
MAT034000
bisacsh
PBWR
thema
515.39
23
515.48
23
Choe, Geon Ho.
author.
aut
http://id.loc.gov/vocabulary/relators/aut
Computational Ergodic Theory
[electronic resource] /
by Geon Ho Choe.
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2005.
XX, 453 p. 250 illus.
online resource.
text
txt
rdacontent
computer
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online resource
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PDF
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Algorithms and Computation in Mathematics,
1431-1550 ;
13
Prerequisites -- Invariant Measures -- The Birkhoff Ergodic Theorem -- The Central Limit Theorem -- More on Ergodicity -- Homeomorphisms of the Circle -- Mod 2 Uniform Distribution -- Entropy -- The Lyapunov Exponent: One-Dimensional Case -- The Lyapunov Exponent: Multidimensional Case -- Stable and Unstable Manifolds -- Recurrence and Entropy -- Recurrence and Dimension -- Data Compression.
Ergodic theory is hard to study because it is based on measure theory, which is a technically difficult subject to master for ordinary students, especially for physics majors. Many of the examples are introduced from a different perspective than in other books and theoretical ideas can be gradually absorbed while doing computer experiments. Theoretically less prepared students can appreciate the deep theorems by doing various simulations. The computer experiments are simple but they have close ties with theoretical implications. Even the researchers in the field can benefit by checking their conjectures, which might have been regarded as unrealistic to be programmed easily, against numerical output using some of the ideas in the book. One last remark: The last chapter explains the relation between entropy and data compression, which belongs to information theory and not to ergodic theory. It will help students to gain an understanding of the digital technology that has shaped the modern information society.
Differentiable dynamical systems.
Engineering mathematics.
Dynamical Systems and Ergodic Theory.
http://scigraph.springernature.com/things/product-market-codes/M1204X
Theoretical, Mathematical and Computational Physics.
http://scigraph.springernature.com/things/product-market-codes/P19005
Mathematical and Computational Engineering.
http://scigraph.springernature.com/things/product-market-codes/T11006
SpringerLink (Online service)
Springer eBooks
Printed edition:
9783540803966
Printed edition:
9783642062070
Printed edition:
9783540231219
Algorithms and Computation in Mathematics,
1431-1550 ;
13
https://doi.org/10.1007/b138894
ZDB-2-SMA
EB
Mathematics and Statistics (Springer-11649)
424990
424990
275579
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MAIN
2017-04-01
EB1131
2018-12-03
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