000			02862nam a22003618i 4500
001			CR9780511976155
003			UkCbUP
005			20200124160233.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			101011s2011||||enk o ||1 0|eng|d
020			_a9780511976155 (ebook)
020			_z9780521888851 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA611.5 _b.D685 2011
082	0	0	_a515/.39 _222
100	1		_aDownarowicz, Tomasz, _d1956- _eauthor.
245	1	0	_aEntropy in Dynamical Systems / _cTomasz Downarowicz.
264		1	_aCambridge : _bCambridge University Press, _c2011.
300			_a1 online resource (xii, 391 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aNew mathematical monographs ; _v18
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0		_aIntroduction -- Part I. Entropy in Ergodic Theory: 1. Shannon information and entropy; 2. Dynamical entropy of a process; 3. Entropy theorems in processes; 4. Kolmogorov-Sinai entropy; 5. The Ergodic Law of Series -- Part II. Entropy in Topological Dynamics: 6. Topological entropy; 7. Dynamics in dimension zero; 8. The entropy structure; 9. Symbolic extensions; 10. A touch of smooth dynamics -- Part III. Entropy Theory for Operators: 11. Measure-theoretic entropy of stochastic operators; 12. Topological entropy of a Markov operator; 13. Open problems in operator entropy -- Appendix A. Toolbox -- Appendix B. Conditional S-M-B.
520			_aThis comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon-McMillan-Breiman Theorem, the Ornstein-Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research.
650		0	_aTopological entropy _vTextbooks.
650		0	_aTopological dynamics _vTextbooks.
776	0	8	_iPrint version: _z9780521888851
830		0	_aNew mathematical monographs ; _v18.
856	4	0	_uhttps://doi.org/10.1017/CBO9780511976155
999			_c517840 _d517838