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Titlebook: Dynamical Systems of Algebraic Origin; Klaus Schmidt Book 1995 Birkh?user Verlag 1995 Group Theory.Lie groups

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發(fā)表于 2025-3-21 16:35:07 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Dynamical Systems of Algebraic Origin
編輯Klaus Schmidt
視頻videohttp://file.papertrans.cn/284/283889/283889.mp4
叢書名稱Progress in Mathematics
圖書封面Titlebook: Dynamical Systems of Algebraic Origin;  Klaus Schmidt Book 1995 Birkh?user Verlag 1995 Group Theory.Lie groups
描述Although the study of dynamical systems is mainly concerned with single trans- formations and one-parameter flows (i. e. with actions of Z, N, JR, or JR+), er- godic theory inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multi-dimensional sym- metry groups. However, the wealth of concrete and natural examples, which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. A remarkable exception is provided by a class of geometric actions of (discrete subgroups of) semi-simple Lie groups, which have led to the discovery of one of the most striking new phenomena in multi-dimensional ergodic theory: under suitable circumstances orbit equivalence of such actions implies not only measurable conjugacy, but the conjugating map itself has to be extremely well behaved. Some of these rigidity properties are inherited by certain abelian subgroups of these groups, but the very special nature of the actions involved does not allow any general conjectures about actions of multi-dimensional abelian groups. Beyond commuting group rotations, commuting toral
出版日期Book 1995
關(guān)鍵詞Group Theory; Lie groups
版次1
doihttps://doi.org/10.1007/978-3-0348-9236-0
isbn_softcover978-3-0348-9957-4
isbn_ebook978-3-0348-9236-0Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightBirkh?user Verlag 1995
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Zero entropy,phisms of a compact, abelian group . to various subgroups Г ? ?.. If . 0, then .) may be positive (even infinite) for certain subgroups Г ? ?. of rank .. For a ?.-action of the form ., where . ? ?. is a prime ideal, this dependence of entropy on the rank of 0413involves the number .(.) introduced in
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0743-1643 N, JR, or JR+), er- godic theory inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multi-dimensional sym- metry groups. However, the wealth of concrete and natural examples, which has contributed so much to the appeal and develop
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Zweck und Ziele der Wirtschaftsinformatik,mical properties, there is an abundance of examples of interesting ?.-actions by automorphisms of compact abelian groups. In this section we introduce a general formalism for the investigation of such actions which will also give us a systematic approach to constructing actions with specified properties.
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