Sufficient conditions for ergodic sensitivity


Xiong Wang - Institute for Advanced Study, Shenzhen University, Nanshan District Shenzhen, Guangdong, P. R. China.
Xinxing Wu - School of Sciences, Southwest Petroleum University, Chengdu, Sichuan, 610500, P. R. China.
Guanrong Chen - Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China.


In this note, some sufficient conditions on the ergodic sensitivity of dynamical systems are obtained, improving the main results in [Q.-L. Huang, Y.-M. Shi, L.-J. Zhang, Appl. Math. Lett., 39 (2015), 31–34] and [R.-S. Li, Y.-M. Shi, Nonlinear Anal., 72 (2010), 2716–2720]. Moreover, it is proved that under these conditions, the second Lyapunov number of a dynamical system is equal to the diameter of its state space.