Furstenberg Families and Sensitivity
Joint Authors
Xiong, Jincheng
Wang, Huoyun
Tan, Feng
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-02-22
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
We introduce and study some concepts of sensitivity via Furstenberg families.
A dynamical system (X,f) is ℱ-sensitive if there exists a positive ε such that for every x∈X and every open neighborhood U of x there exists y∈U such that the pair (x,y) is not ℱ-ε-asymptotic; that is, the time set {n:d(fn(x),fn(y))>ε} belongs to ℱ, where ℱ is a Furstenberg family.
A dynamical system (X,f) is (ℱ1, ℱ2)-sensitive if there is a positive ε such that every x∈X is a limit of points y∈X such that the pair (x,y) is ℱ1-proximal but not ℱ2-ε-asymptotic; that is, the time set {n:d(fn(x),fn(y))<δ} belongs to ℱ1 for any positive δ but the time set {n:d(fn(x),fn(y))>ε} belongs to ℱ2, where ℱ1 and ℱ2 are Furstenberg families.
American Psychological Association (APA)
Wang, Huoyun& Xiong, Jincheng& Tan, Feng. 2010. Furstenberg Families and Sensitivity. Discrete Dynamics in Nature and Society،Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-488121
Modern Language Association (MLA)
Wang, Huoyun…[et al.]. Furstenberg Families and Sensitivity. Discrete Dynamics in Nature and Society No. 2010 (2010), pp.1-12.
https://search.emarefa.net/detail/BIM-488121
American Medical Association (AMA)
Wang, Huoyun& Xiong, Jincheng& Tan, Feng. Furstenberg Families and Sensitivity. Discrete Dynamics in Nature and Society. 2010. Vol. 2010, no. 2010, pp.1-12.
https://search.emarefa.net/detail/BIM-488121
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-488121