000			03137nam a22005175i 4500
001			978-3-540-27305-9
003			DE-He213
005			20161121230933.0
007			cr nn 008mamaa
008			100301s2005 gw | s |||| 0|eng d
020			_a9783540273059 _9978-3-540-27305-9
024	7		_a10.1007/b138894 _2doi
050		4	_aQA313
072		7	_aPBWR _2bicssc
072		7	_aMAT034000 _2bisacsh
082	0	4	_a515.39 _223
082	0	4	_a515.48 _223
100	1		_aChoe, Geon Ho. _eauthor.
245	1	0	_aComputational Ergodic Theory _h[electronic resource] / _cby Geon Ho Choe.
264		1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2005.
300			_aXX, 453 p. 250 illus. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aAlgorithms and Computation in Mathematics, _x1431-1550 ; _v13
505	0		_aPrerequisites -- 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.
520			_aErgodic 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.
650		0	_aMathematics.
650		0	_aDynamics.
650		0	_aErgodic theory.
650		0	_aPhysics.
650		0	_aApplied mathematics.
650		0	_aEngineering mathematics.
650	1	4	_aMathematics.
650	2	4	_aDynamical Systems and Ergodic Theory.
650	2	4	_aTheoretical, Mathematical and Computational Physics.
650	2	4	_aAppl.Mathematics/Computational Methods of Engineering.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9783540231219
830		0	_aAlgorithms and Computation in Mathematics, _x1431-1550 ; _v13
856	4	0	_uhttp://dx.doi.org/10.1007/b138894
912			_aZDB-2-SMA
950			_aMathematics and Statistics (Springer-11649)
999			_c506139 _d506139