Inverse Limits And Dynamical Systems
Abstract
This chapter discusses the inverse limits and dynamical systems. If X1,X2,X3, is a sequence of metric spaces and f1, f2, f3, is a sequence of mappings, such that fi: Xi+1 →Xi for i = 1, 2, 3,., by the inverse limit of the inverse limit sequence {Xi, fi} is meant the subset of the product space Πi0Xi that contains the point (x1, x2, x3,.) if and only if fi(xi+1) =xi for each positive integer i. The inverse limit of the inverse limit sequence {Xi, fi} is denoted by lim {Xi, fi}. For convenience of notation, boldface characters are used to denote sequences. The chapter elaborates the concepts related to characterization of chainability, plane embedding, inverse limits on [0, 1], and the property of Kelley. Inverse limits with upper semi-continuous bonding functions and the applications of inverse limits in economics are also discussed in the chapter. © 2007 Elsevier B.V. All rights reserved.
Recommended Citation
W. T. Ingram, "Inverse Limits And Dynamical Systems," Open Problems in Topology II, pp. 289 - 301, Elsevier, Dec 2007.
The definitive version is available at https://doi.org/10.1016/B978-044452208-5/50033-8
Department(s)
Mathematics and Statistics
International Standard Book Number (ISBN)
978-044452208-5
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2023 Elsevier, All rights reserved.
Publication Date
01 Dec 2007
