Recurrence in topological dynamics : (Record no. 1431312)

MARC details
000 -LEADER
fixed length control field 02347cam a2200241 a 4500
001 - CONTROL NUMBER
control field 4489609
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20250602151535.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 970604s1997 nyua b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780306455506
040 ## - CATALOGING SOURCE
Original cataloging agency CSL
Transcribing agency CSL
084 ## - COLON CLASSIFICATION NUMBER
Classification number B316z7 N7 NBHM
Assigning agency CSL
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Akin, Ethan.
Dates associated with a name 1946-
9 (RLIN) 811421
245 10 - TITLE STATEMENT
Title Recurrence in topological dynamics :
Remainder of title Furstenberg families and Ellis actions
260 ## - PUBLICATION, DISTRIBUTION, ETC.
Place of publication, distribution, etc. New York :
Name of publisher, distributor, etc. Plenum Press,
Date of publication, distribution, etc. 1997.
300 ## - PHYSICAL DESCRIPTION
Extent ix, 265 p. :
Other physical details ill. ;
Dimensions 24 cm.
490 1# - SERIES STATEMENT
Series statement The university series in mathematics
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc. note Includes bibliographical references and index.
520 ## - SUMMARY, ETC.
Summary, etc. 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 natural constructions arise from a topology or group action on the underlying set. The foundations are laid, in perhaps tedious detail, in Chapter 2. The family machinery is then applied in Chapters 3 and 4 to describe family versions of recurrence, topological transitivity, distality and rigidity.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Topological dynamics.
9 (RLIN) 811422
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Point mappings (Mathematics)
9 (RLIN) 811423
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title University series in mathematics
9 (RLIN) 811424
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme Colon Classification (CC)
Suppress in OPAC No
Koha item type Textual
Classification part B316z7 N7 NBHM
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Home library Current library Date acquired Source of acquisition Total Checkouts Full call number Barcode Date last seen Price effective from Koha item type
    Colon Classification (CC)     Central Science Library Faculty of Mathematical Sciences Library 2025-01-13 New India Book Agency   B316z7 N7 NBHM SL1656215 2025-06-02 2025-06-02 Textual
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