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Titlebook: Ergodic Theory; with a view towards Manfred Einsiedler,Thomas Ward Textbook 2011 Springer-Verlag London Limited 2011 Ergodic theory.Homoge

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書目名稱Ergodic Theory
副標(biāo)題with a view towards
編輯Manfred Einsiedler,Thomas Ward
視頻videohttp://file.papertrans.cn/315/314487/314487.mp4
概述With a rigorous development of basic ergodic theory and homogeneous dynamics, no background in Ergodic theory or Lie theory is assumed Offers both complete and motivated treatments of Weyl and Szemere
叢書名稱Graduate Texts in Mathematics
圖書封面Titlebook: Ergodic Theory; with a view towards  Manfred Einsiedler,Thomas Ward Textbook 2011 Springer-Verlag London Limited 2011 Ergodic theory.Homoge
描述.This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence..Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl‘s polynomial equidistribution theorem, the ergodic proof of Szemeredi‘s theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits..Ergodic Theory with a view towards Number Theory. will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
出版日期Textbook 2011
關(guān)鍵詞Ergodic theory; Homogenous spaces; Measure rigidity; Number theory
版次1
doihttps://doi.org/10.1007/978-0-85729-021-2
isbn_softcover978-1-4471-2591-4
isbn_ebook978-0-85729-021-2Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer-Verlag London Limited 2011
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Ergodicity, Recurrence and Mixing,tionship between various mixing properties is described. The mean and pointwise ergodic theorems are proved. An approach to the maximal ergodic theorem via a covering lemma is given, which will be extended in Chapter 8 to more general group actions.
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,Furstenberg’s Proof of Szemerédi’s Theorem,pters 5 and 6 to give a careful proof of Furstenberg’s multiple recurrence theorem. To help motivate the proof we consider several special cases first, including the case of weak-mixing and discrete spectrum systems, and Roth’s theorem. A simple proof of van der Waerden’s theorem is given, and we sh
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Actions of Locally Compact Groups,p automorphisms are introduced, and their mixing properties described. Some of the basic machinery of the ergodic theory of groups actions is developed: Haar measures, regular representations, amenability, mean ergodic theorems and the ergodic decomposition. The pointwise ergodic theorem is proved f
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