Acta mathematica scientia, Series B >
ON F-SENSITIVE PAIRS
Received date: 2009-07-30
Revised date: 2010-03-15
Online published: 2011-07-20
Supported by
The first author is supported by NSFC (10771079;
10871186; 11071084; 11026095) and NSF of Guangdong Province (10451063101006332). The second author is
partially supported by NSFC (11001071) and Hefei University of Technology (GDBJ2008-024; 2010HGXJ0200).
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.
Key words： sensitive pair; Furstenberg family; transitive system
TAN Feng , ZHANG Rui-Feng . ON F-SENSITIVE PAIRS[J]. Acta mathematica scientia, Series B, 2011 , 31(4) : 1425 -1435 . DOI: 10.1016/S0252-9602(11)60328-7
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