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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Habituate

Girish Mahajan,Lakshmi Balachandranus spaces by studying the geodesic flow on hyperbolic surfaces. Since we do not assume any prior knowledge of Lie theory or differential geometry, the material needed is introduced here. As an application, the geodesic flow is used to give another proof of ergodicity for the Gauss measure from Chapter 3.

NADIR

Jan Wilschut,Janny Scholma,Toon Stegmannorocycle flow, and go on to deduce from mixing of the geodesic flow a form of unique ergodicity for the horocycle flow. We use this, together with the ergodic decomposition, to establish equidistribution for orbits of the horocycle flow.

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Motivation,ticular to problems in number theory. This chapter introduces some of the important examples needed, and states some of the theorems arising from ergodic theory that will be discussed in this volume. We also discuss ergodic theory in more general terms.

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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.

GROVE

政府

Geodesic Flow on Quotients of the Hyperbolic Plane,us spaces by studying the geodesic flow on hyperbolic surfaces. Since we do not assume any prior knowledge of Lie theory or differential geometry, the material needed is introduced here. As an application, the geodesic flow is used to give another proof of ergodicity for the Gauss measure from Chapter 3.

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Esalate

Manfred Einsiedler,Thomas WardWith 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

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Graduate Texts in Mathematicshttp://image.papertrans.cn/e/image/314487.jpg