数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (4): 1425-1435.doi: 10.1016/S0252-9602(11)60328-7
谭枫|张瑞丰
TAN Feng, ZHANG Rui-Feng
摘要:
In the present paper, we define sensitive pairs via Furstenberg families and
discuss the relation of three definitions: sensitivity, F-sensitivity and F-sensitive pairs,
see Theorem 1. For transitive systems, we give some su?cient conditions to ensure the
existence of F-sensitive pairs. In particular, each non-minimal E system (M system, P sys-
tem) has positive lower density (Fs, Fr resp.)-sensitive pairs almost everywhere. Moreover,
each non-minimal M system is Fts-sensitive. Finally, by some examples we show that: (1)
F-sensitivity can not imply the existence of F-sensitive pairs. That means there exists an
F-sensitive system, which has no F-sensitive pairs. (2) There is no immediate relation be-
tween the existence of sensitive pairs and Li-Yorke chaos, i.e., there exists a system (X,f)
without Li-Yorke scrambled pairs, which has κB-sensitive pairs almost everywhere. (3)
If the system (G,f) is sensitive, where G is a finite graph, then it has κB-sensitive pairs
almost everywhere.
中图分类号: