{"product_id":"typical-dynamics-of-volume-preserving-homeomorphisms-paperback-9780521172431","title":"Typical Dynamics of Volume Preserving Homeomorphisms (Paperback) 9780521172431","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eTypical Dynamics of Volume Preserving Homeomorphisms\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eA self-contained introduction to typical properties of volume preserving homeomorphisms.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eSteve Alpern (Author), V. S. Prasad (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9780521172431, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback, published 17 February 2011\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e238 pages\u003cbr\u003e22.9 x 15.2 x 1.4 cm, 0.35 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003eReview of the hardback: 'The authors of this book are undoubtedly the experts of generic properties of measure preserving homeomorphisms of compact and locally compact manifolds, continuing and extending ground-breaking early work by J. C. Oxtoby and S. M. Ulam. The book is very well and carefully written and is an invaluable reference for anybody working on the interface between topological dymanics and ergodic theory.' Monatshefte für Mathematik\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eThis 2000 book provides a self-contained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit n-dimensional cube, and they go on to prove fixed point theorems (Conley–Zehnder– Franks). This is done in a number of short self-contained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHistorical Preface\u003cbr\u003e General outline\u003cbr\u003e Part I. Volume Preserving Homomorphisms of the Cube: 1. Introduction to Parts I and II (compact manifolds)\u003cbr\u003e 2. Measure preserving homeomorphisms\u003cbr\u003e 3. Discrete approximations\u003cbr\u003e 4. Transitive homeomorphisms of In and Rn\u003cbr\u003e 5. Fixed points and area preservation\u003cbr\u003e 6. Measure preserving Lusin theorem\u003cbr\u003e 7. Ergodic homeomorphisms\u003cbr\u003e 8. Uniform approximation in G[In, ?] and generic properties in ?[In, ?]\u003cbr\u003e Part II. Measure Preserving Homeomorphisms of a Compact Manifold: 9. Measures on compact manifolds\u003cbr\u003e 10. Dynamics on compact manifolds\u003cbr\u003e Part III. Measure Preserving Homeomorphisms of a Noncompact Manifold: 11.  Introduction to Part III\u003cbr\u003e 12. Ergodic volume preserving homeomorphisms of Rn\u003cbr\u003e 13. Manifolds where ergodic is not generic\u003cbr\u003e 14. Noncompact manifolds and ends\u003cbr\u003e 15. Ergodic homeomorphisms: the results\u003cbr\u003e 16. Ergodic homeomorphisms: proof\u003cbr\u003e 17. Other properties typical in M[X, ?]\u003cbr\u003e Appendix 1. Multiple Rokhlin towers and conjugacy approximation\u003cbr\u003e Appendix 2. Homeomorphic measures\u003cbr\u003e Bibliography\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Probability \u0026amp; statistics [\u003ca title=\"See our other books on Probability \u0026amp; statistics\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Probability%20\u0026amp;%20statistics%20%5BPBT%5D%22\"\u003ePBT\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":46006751985944,"sku":"9780521172431","price":33.99,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9780521172431i_ffcd5150-bec9-494f-8589-3558632d7434.jpg?v=1691372955","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/typical-dynamics-of-volume-preserving-homeomorphisms-paperback-9780521172431","provider":"Freshly Printed Books","version":"1.0","type":"link"}