an:06537084
Zbl 1332.54203
Niu, Yingxuan; Su, Shoubao; Zhou, Benda
Strong sensitivity of systems satisfying the large deviations theorem
EN
Int. J. Gen. Syst. 44, No. 1, 98-105 (2015).
00342383
2015
j
54H20
topologically strong ergodicity; sensitivity; upper density one sensitivity; positive lower density sensitivity; ergodic sensitivity; the large deviations theorem
Summary: Let \(f\) be a continuous map from a compact metric space \(X\) to itself. In this paper, We introduce two concepts of upper density one sensitivity and positive lower density sensitivity, and prove that (1) if \(f\) is a topologically strongly ergodic map, then it is upper density one sensitive; (2) if \(f\) is a sensitive map satisfying the large deviations theorem, then \(f\) is positive lower density sensitive.