Dynamical Systems and Semisimple Groups: An Introduction (Cambridge Tracts in Mathematics)

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9780521142168: Dynamical Systems and Semisimple Groups: An Introduction (Cambridge Tracts in Mathematics)

Here is an introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups. The main goal is to serve as an entry into the current literature on the ergodic theory of measure preserving actions of semisimple Lie groups for students who have taken the standard first year graduate courses in mathematics. The author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts normally covered in first courses on manifolds and Lie groups plus topics such as integration of infinitesimal actions of Lie groups. He then derives the basic structure theorems for the real semisimple Lie groups, such as the Cartan and Iwasawa decompositions and gives an extensive exposition of the general facts and concepts from topological dynamics and ergodic theory, including detailed proofs of the multiplicative ergodic theorem and Moore's ergodicity theorem. This book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems.

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Book Description:

The theory of dynamical systems can be described as the study of the global properties of groups of transformations. The historical roots of the subject lie in celestial and statistical mechanics, for which the group is the time parameter. The more general modern theory treats the dynamical properties of the semisimple Lie groups. Some of the most fundamental discoveries in this area are due to the work of G.A. Margulis and R. Zimmer. This book comprises a systematic, self-contained introduction to the Margulis-Zimmer theory, and provides an entry into current research. Assuming only a basic knowledge of manifolds, algebra, and measure theory, this book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems.

Review:

"Well written and...highly recommended." Bulletin of the American Mathematical Society

"...excellent and quite comprehensive introduction to the algebra and dynamics of Lie group actions in the chapters..." Monatshefte fur Mathematik

"An important feature of the text is the inclusion of many exercises, always a helpful thing." Proceedings of the Edinburgh Mathematical Society

"...nicely written and highly recommended, especially for graduate students specializing in Lie groups and ergodic theory." Mathematical Reviews

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Buchbeschreibung CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2010. Paperback. Buchzustand: New. Language: English . Brand New Book ***** Print on Demand *****.This 1998 book provides an introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups. The main goal is to serve as an entry into the literature on the ergodic theory of measure preserving actions of semisimple Lie groups. The author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts on manifolds and Lie groups plus topics such as integration of infinitesimal actions of Lie groups. He then derives the basic structure theorems for the real semisimple Lie groups, such as the Cartan and Iwasawa decompositions and gives an extensive exposition of the general facts and concepts from topological dynamics and ergodic theory, including detailed proofs of the multiplicative ergodic theorem and Moore s ergodicity theorem. This book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems. Buchnummer des Verkäufers AAV9780521142168

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Buchbeschreibung CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2010. Paperback. Buchzustand: New. Language: English . Brand New Book ***** Print on Demand *****. This 1998 book provides an introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups. The main goal is to serve as an entry into the literature on the ergodic theory of measure preserving actions of semisimple Lie groups. The author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts on manifolds and Lie groups plus topics such as integration of infinitesimal actions of Lie groups. He then derives the basic structure theorems for the real semisimple Lie groups, such as the Cartan and Iwasawa decompositions and gives an extensive exposition of the general facts and concepts from topological dynamics and ergodic theory, including detailed proofs of the multiplicative ergodic theorem and Moore s ergodicity theorem. This book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems. Buchnummer des Verkäufers AAV9780521142168

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Buchbeschreibung 2010. Paperback. Buchzustand: NEW. 9780521142168 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Buchnummer des Verkäufers HTANDREE0448237

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Buchbeschreibung Cambridge University Press. Paperback. Buchzustand: New. Paperback. 264 pages. Dimensions: 8.9in. x 6.1in. x 0.7in.Here is an introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups. The main goal is to serve as an entry into the current literature on the ergodic theory of measure preserving actions of semisimple Lie groups for students who have taken the standard first year graduate courses in mathematics. The author develops in a detailed and self-contained way the main results on Lie groups, Lie algebras, and semisimple groups, including basic facts normally covered in first courses on manifolds and Lie groups plus topics such as integration of infinitesimal actions of Lie groups. He then derives the basic structure theorems for the real semisimple Lie groups, such as the Cartan and Iwasawa decompositions and gives an extensive exposition of the general facts and concepts from topological dynamics and ergodic theory, including detailed proofs of the multiplicative ergodic theorem and Moores ergodicity theorem. This book should appeal to anyone interested in Lie theory, differential geometry and dynamical systems. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Buchnummer des Verkäufers 9780521142168

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Buchbeschreibung Cambridge University Press, 2010. Paperback. Buchzustand: New. book. Buchnummer des Verkäufers M0521142164

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Buchbeschreibung Cambridge University Press, 2017. Paperback. Buchzustand: New. Never used! This item is printed on demand. Buchnummer des Verkäufers P110521142164

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