TY - JOUR
T1 - Central limit theorem and chaoticity
AU - Wu, Xinxing
AU - Chen, Guanrong
PY - 2014/9
Y1 - 2014/9
N2 - This paper studies the relations between stochastic properties and chaotic properties of a dynamical system satisfying the central limit theorem. For such a system, it is proved that every nonempty open set in its defining space contains a point with positive lower density of its return time set and that the system is syndetically sensitive, provided that it is strongly topologically ergodic. Moreover, it is shown that the system admits many chaotic properties if its domain is restricted to a tree. © 2014 Elsevier B.V.
AB - This paper studies the relations between stochastic properties and chaotic properties of a dynamical system satisfying the central limit theorem. For such a system, it is proved that every nonempty open set in its defining space contains a point with positive lower density of its return time set and that the system is syndetically sensitive, provided that it is strongly topologically ergodic. Moreover, it is shown that the system admits many chaotic properties if its domain is restricted to a tree. © 2014 Elsevier B.V.
KW - Strongly topologically ergodic
KW - Syndetic sensitivity
KW - Syndetically ergodic
KW - The central limit theorem
KW - Urysohn's Lemma
UR - http://www.scopus.com/inward/record.url?scp=84902333708&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84902333708&origin=recordpage
U2 - 10.1016/j.spl.2014.05.017
DO - 10.1016/j.spl.2014.05.017
M3 - 21_Publication in refereed journal
VL - 92
SP - 137
EP - 142
JO - Statistics and Probability Letters
JF - Statistics and Probability Letters
SN - 0167-7152
ER -