LEADER 03735nam 22006852 450 001 9910781866603321 005 20151005020621.0 010 $a1-107-21931-0 010 $a1-283-38392-6 010 $a1-139-18928-X 010 $a9786613383921 010 $a1-139-18798-8 010 $a1-139-19058-X 010 $a1-139-18336-2 010 $a1-139-18567-5 010 $a0-511-97615-1 035 $a(CKB)2550000000061344 035 $a(EBL)807302 035 $a(OCoLC)782877021 035 $a(SSID)ssj0000634728 035 $a(PQKBManifestationID)11382921 035 $a(PQKBTitleCode)TC0000634728 035 $a(PQKBWorkID)10643776 035 $a(PQKB)10979778 035 $a(UkCbUP)CR9780511976155 035 $a(MiAaPQ)EBC807302 035 $a(Au-PeEL)EBL807302 035 $a(CaPaEBR)ebr10521005 035 $a(CaONFJC)MIL338392 035 $a(PPN)261277545 035 $a(EXLCZ)992550000000061344 100 $a20101011d2011|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aEntropy in Dynamical Systems /$fTomasz Downarowicz$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2011. 215 $a1 online resource (xii, 391 pages) $cdigital, PDF file(s) 225 1 $aNew mathematical monographs ;$v18 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-88885-9 320 $aIncludes bibliographical references (p. [379]-385) and index. 327 $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. 330 $aThis comprehensive text on entropy covers three major types of dynamics: measure preserving transformations; continuous maps on compact spaces; and operators on function spaces. Part I contains proofs of the Shannon-McMillan-Breiman Theorem, the Ornstein-Weiss Return Time Theorem, the Krieger Generator Theorem and, among the newest developments, the ergodic law of series. In Part II, after an expanded exposition of classical topological entropy, the book addresses symbolic extension entropy. It offers deep insight into the theory of entropy structure and explains the role of zero-dimensional dynamics as a bridge between measurable and topological dynamics. Part III explains how both measure-theoretic and topological entropy can be extended to operators on relevant function spaces. Intuitive explanations, examples, exercises and open problems make this an ideal text for a graduate course on entropy theory. More experienced researchers can also find inspiration for further research. 410 0$aNew mathematical monographs ;$v18. 606 $aTopological entropy$vTextbooks 606 $aTopological dynamics$vTextbooks 615 0$aTopological entropy 615 0$aTopological dynamics 676 $a515/.39 686 $aMAT000000$2bisacsh 700 $aDownarowicz$b Tomasz$f1956-$01554368 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910781866603321 996 $aEntropy in Dynamical Systems$93815576 997 $aUNINA