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Titlebook: Recurrence in Topological Dynamics; Furstenberg Families Ethan Akin Book 1997 Springer-Verlag US 1997 Compactification.DEX.Volume.dynamical

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發(fā)表于 2025-3-21 17:11:14 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Recurrence in Topological Dynamics
副標(biāo)題Furstenberg Families
編輯Ethan Akin
視頻videohttp://file.papertrans.cn/825/824336/824336.mp4
叢書名稱University Series in Mathematics
圖書封面Titlebook: Recurrence in Topological Dynamics; Furstenberg Families Ethan Akin Book 1997 Springer-Verlag US 1997 Compactification.DEX.Volume.dynamical
描述In the long run of a dynamical system, after transient phenomena have passed away, what remains is recurrence. An orbit is recurrent when it returns repeatedly to each neighborhood of its initial position. We can sharpen the concept by insisting that the returns occur with at least some prescribed frequency. For example, an orbit lies in some minimal subset if and only if it returns almost periodically to each neighborhood of the initial point. That is, each return time set is a so-called syndetic subset ofT= the positive reals (continuous time system) or T = the positive integers (discrete time system). This is a prototype for many of the results in this book. In particular, frequency is measured by membership in a family of subsets of the space modeling time, in this case the family of syndetic subsets of T. In applying dynamics to combinatorial number theory, Furstenberg introduced a large number of such families. Our first task is to describe explicitly the calculus of families implicit in Furstenberg‘s original work and in the results which have proliferated since. There are general constructions on families, e. g. , the dual of a family and the product of families. Other natu
出版日期Book 1997
關(guān)鍵詞Compactification; DEX; Volume; dynamical systems; ergodic theory; ergodicity; mixing; number theory; semigro
版次1
doihttps://doi.org/10.1007/978-1-4757-2668-8
isbn_softcover978-1-4419-3272-3
isbn_ebook978-1-4757-2668-8
copyrightSpringer-Verlag US 1997
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沙發(fā)
發(fā)表于 2025-3-21 21:10:00 | 只看該作者
Monoid Actions,ly continuous maps. The .,the set of uniformly continuous pseudometrics, provides an equivalent characterization. Recall that a uniformity is metrizable iff it has a countable base. Also a compact space has a unique uniformity consisting of all neighborhoods of the diagonal.
板凳
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地板
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Book 1997epeatedly to each neighborhood of its initial position. We can sharpen the concept by insisting that the returns occur with at least some prescribed frequency. For example, an orbit lies in some minimal subset if and only if it returns almost periodically to each neighborhood of the initial point. T
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發(fā)表于 2025-3-22 11:00:25 | 只看該作者
Introduction,t point of ., when . is a limit point of the orbit sequence {..(.) : . ∈ .} where . is the set of nonnegative integers. This means that the sequence enters every neighborhood of . infinitely often. That is, for any open set . containing ., the entrance time set .(.) = {. ∈ . : ..(.) ∈ .} is infinite
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發(fā)表于 2025-3-22 15:18:41 | 只看該作者
Monoid Actions, in fact the class of subspaces of compact Hausdorff spaces. It is also the class of spaces whose topology can be associated with some Hausdorff uniformity. We follow Kelley (1955) in using uniformities, distinguished collections of neighborhoods of the diagonal, to define uniform spaces and uniform
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發(fā)表于 2025-3-22 17:55:21 | 只看該作者
Compactifications, linear operator .: .. → .. between . spaces, the operator norm of . can be described as:.Of course by linearity . for all x ∈ ... The set .(.., ..) of all such bounded linear operators is a . space with the operator norm, and its unit ball is the set of operators of norm at most 1. Equivalently:..
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發(fā)表于 2025-3-23 03:59:41 | 只看該作者
Introduction,t point of ., when . is a limit point of the orbit sequence {..(.) : . ∈ .} where . is the set of nonnegative integers. This means that the sequence enters every neighborhood of . infinitely often. That is, for any open set . containing ., the entrance time set .(.) = {. ∈ . : ..(.) ∈ .} is infinite.
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發(fā)表于 2025-3-23 09:11:14 | 只看該作者
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