Stronger Forms of Sensitivity for Measure-Preserving Maps and Semiflows on Probability Spaces
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-07
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
This paper is concerned with some stronger forms of sensitivity for measure-preserving maps and semiflows on probability spaces.
A new form of sensitivity is introduced, called ergodic sensitivity.
It is shown that, on a metric probability space with a fully supported measure, if a measure-preserving map is weak mixing, then it is ergodically sensitive and multisensitive; and if it is strong mixing, then it is cofinitely sensitive, where it is not required that the map is continuous and the space is compact.
Similar results for measure-preserving semiflows are obtained, where it is required in a result about ergodic sensitivity that the space is compact in some sense and the semiflow is continuous.
In addition, relationships between some sensitive properties of a map and its iterations are discussed, including syndetic sensitivity, cofinite sensitivity, ergodic sensitivity as well as usual sensitivity, n-sensitivity, and multisensitivity.
Moreover, it is shown that multisensitivity, cofinite sensitivity, and ergodic sensitivity can be lifted up by a semiopen factor map.
American Psychological Association (APA)
Li, Risong& Shi, Yuming. 2014. Stronger Forms of Sensitivity for Measure-Preserving Maps and Semiflows on Probability Spaces. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1014752
Modern Language Association (MLA)
Li, Risong& Shi, Yuming. Stronger Forms of Sensitivity for Measure-Preserving Maps and Semiflows on Probability Spaces. Abstract and Applied Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1014752
American Medical Association (AMA)
Li, Risong& Shi, Yuming. Stronger Forms of Sensitivity for Measure-Preserving Maps and Semiflows on Probability Spaces. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1014752
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014752