{"product_id":"entropy-in-dynamical-systems-hardback-9780521888851","title":"Entropy in Dynamical Systems (Hardback) 9780521888851","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eEntropy in Dynamical Systems\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA comprehensive course on entropy in dynamical systems ideal for graduate students learning the subject from scratch.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eTomasz Downarowicz (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521888851, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 12 May 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e404 pages, 30 b\/w illus.  80 exercises\u003cbr\u003e23.5 x 16 x 2.5 cm, 0.69 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e\"Overall the writing is clear and the author has included motivational and expository material, as well as some examples and exercises. The presentation is nicely unified, and the different parts of the book interact well.\"  \u003cbr\u003eMichael Hochman, Mathematical Reviews\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis 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.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e Part I. Entropy in Ergodic Theory: 1. Shannon information and entropy\u003cbr\u003e 2. Dynamical entropy of a process\u003cbr\u003e 3. Entropy theorems in processes\u003cbr\u003e 4. Kolmogorov–Sinai entropy\u003cbr\u003e 5. The ergodic law of series\u003cbr\u003e Part II. Entropy in Topological Dynamics: 6. Topological entropy\u003cbr\u003e 7. Dynamics in dimension zero\u003cbr\u003e 8. The entropy structure\u003cbr\u003e 9. Symbolic extensions\u003cbr\u003e 10. A touch of smooth dynamics\u003cbr\u003e Part III. Entropy Theory for Operators: 11. Measure theoretic entropy of stochastic operators\u003cbr\u003e 12. Topological entropy of a Markov operator\u003cbr\u003e 13. Open problems in operator entropy\u003cbr\u003e Appendix A. Toolbox\u003cbr\u003e Appendix B. Conditional S-M-B\u003cbr\u003e List of symbols\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Nonlinear science [\u003ca title=\"See our other books on Nonlinear science\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Nonlinear%20science%20%5BPBWR%5D%22\"\u003ePBWR\u003c\/a\u003e], Differential calculus \u0026amp; equations [\u003ca title=\"See our other books on Differential calculus \u0026amp; equations\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Differential%20calculus%20\u0026amp;%20equations%20%5BPBKJ%5D%22\"\u003ePBKJ\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265358352664,"sku":"9780521888851","price":75.89,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521888851i.jpg?v=1692022078","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/entropy-in-dynamical-systems-hardback-9780521888851","provider":"Freshly Printed Books","version":"1.0","type":"link"}