{"product_id":"nilpotent-structures-in-ergodic-theory-9781470447809","title":"Nilpotent Structures in Ergodic Theory","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eNilsystems play a key role in the structure theory of measure preserving systems, arising as the natural objects that describe the behaviour of multiple ergodic averages. This book provides a comprehensive treatment of their role in ergodic theory.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cul\u003e\n\u003cli\u003eIntroduction\u003c\/li\u003e\n\u003cli\u003ePart 1. Basics: Background material\u003c\/li\u003e\n\u003cli\u003eDynamical background\u003c\/li\u003e\n\u003cli\u003eRotations\u003c\/li\u003e\n\u003cli\u003eGroup extensions\u003c\/li\u003e\n\u003cli\u003ePart 2. Cubes: Cubes in an algebraic setting\u003c\/li\u003e\n\u003cli\u003eDynamical cubes\u003c\/li\u003e\n\u003cli\u003eCubes in ergodic theory\u003c\/li\u003e\n\u003cli\u003eThe structure factors\u003c\/li\u003e\n\u003cli\u003ePart 3. Nilmanifolds and nilsystems: Nilmanifolds\u003c\/li\u003e\n\u003cli\u003eNilsystems\u003c\/li\u003e\n\u003cli\u003eCubic structures in nilmanifolds\u003c\/li\u003e\n\u003cli\u003eFactors of nilsystems\u003c\/li\u003e\n\u003cli\u003ePolynomials in nilmanifolds and nilsystems\u003c\/li\u003e\n\u003cli\u003eArithmetic progressions in nilsystems\u003c\/li\u003e\n\u003cli\u003ePart 4. Structure theorems: The ergodic structure theorem\u003c\/li\u003e\n\u003cli\u003eOther structure theorems\u003c\/li\u003e\n\u003cli\u003eRelations between consecutive factors\u003c\/li\u003e\n\u003cli\u003eThe structure theorem in a particular case\u003c\/li\u003e\n\u003cli\u003eThe structure theorem in the general case\u003c\/li\u003e\n\u003cli\u003ePart 5. Applications: The method of characteristic factors\u003c\/li\u003e\n\u003cli\u003eUniformity seminorms on $\\ell^\\infty$ and pointwise convergence of cubic averages\u003c\/li\u003e\n\u003cli\u003eMultiple correlations, good weights, and anti-uniformity\u003c\/li\u003e\n\u003cli\u003eInverse results for uniformity seminorms and applications\u003c\/li\u003e\n\u003cli\u003eThe comparison method\u003c\/li\u003e\n\u003cli\u003eBibliography\u003c\/li\u003e\n\u003cli\u003eIndex of terms\u003c\/li\u003e\n\u003cli\u003eIndex of symbols.\u003c\/li\u003e\n\u003cli\u003e\u003cul\u003e\u003c\/ul\u003e\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"MP-AMM American Mathematical","offers":[{"title":"Default Title","offer_id":50041344196951,"sku":"9781470447809","price":103.5,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781470447809.jpg?v=1740182874","url":"https:\/\/bookcurl.com\/products\/nilpotent-structures-in-ergodic-theory-9781470447809","provider":"Book Curl","version":"1.0","type":"link"}