Thickly Syndetical Sensitivity of Topological Dynamical System
Consider the surjective continuous map f:X→X, where X is a compact metric space. In this paper we give several stronger versions of sensitivity, such as thick sensitivity, syndetic sensitivity, thickly syndetic sensitivity, and strong sensitivity. We establish the following. (1) If (X,f) is minimal...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/583431 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Consider the surjective continuous map f:X→X, where X is a compact metric space. In this paper we give several stronger versions of sensitivity, such as thick sensitivity, syndetic sensitivity, thickly syndetic sensitivity, and strong sensitivity. We establish the following. (1) If (X,f) is minimal and sensitive, then (X,f) is syndetically sensitive. (2) Weak mixing implies thick sensitivity. (3) If (X,f) is minimal and weakly mixing, then it is thickly syndetically sensitive. (4) If (X,f) is a nonminimal M-system, then it is thickly syndetically sensitive. Devaney chaos implies thickly periodic sensitivity. (5) We give a syndetically sensitive system which is not thickly sensitive. (6) We give thickly syndetically sensitive examples but not cofinitely sensitive ones. |
|---|---|
| ISSN: | 1026-0226 1607-887X |