References
- C. Abraham, G. Biau, and B. Cadre, Chaotic properties of mapping on a probability space, J. Math. Anal. Appl. 266 (2002), pp. 420–431.
- D. Ahmadi Dastjerdi and M. Hosseini, Sub-shadowings, Nonlinear Anal. 72 (2010), pp. 3759–3766.
- J. Bank, J. Brooks, G. Cairns, G. Davis, and D. Stacey, On Devaney's definition of chaos, Amer. Math. Monthly 99 (1992), pp. 332–334.
- E. Glasner and B. Weiss, Sensitive dependence on initial conditions, Nonlinearity 6 (1993), pp. 1067–1075.
- R. Gu, The large deviations theorem and ergodicity, Chaos Solitons Fractals 34 (2007), pp. 1387–1392.
- B. Hasselblatt and A. Katok, A First Course in Dynamics, Cambridge University Press, New York, 2003.
- L. He, X. Yan, and L. Wang, Weak-mixing implies sensitive dependence, J. Math. Anal. Appl. 299 (2004), pp. 300–304.
- H. Kato, Everywhere chaotic homeomorphisms on manifolds and k −dimensional merger manifolds, Topology Appl. 72 (1996), pp. 1–17.
- S. Lardjane, On some stochastic properties in Devaney's chaos, Chaos Solitons Fractals 28 (2006), pp. 668–672.
- R. Li, A note on stronger forms of sensitivity for dynamical systems, Chaos Solitons Fractals 45 (2012), pp. 753–758.
- R. Li, The large deviations theorem and ergodic sensitivity, Commun. Nonlinear Sci. Numer. Simul. 18 (2013), pp. 819–825.
- R. Li, A note on shadowing with chain transitivity, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), pp. 2815–2823.
- R. Li and Y. Shi, Several sufficient conditions for sensitive dependence on initial conditions, Nonlinear Anal. 72 (2010), pp. 2716–2720.
- V.V. Nemiskii and V.V. Stepanov, Qualitative Theory of Ordinary Differential Equations, Princeton Univ. Press, Princeton, NJ, 1960.
- Y. Niu, The average-shadowing property and strong ergodicity, J. Math. Anal. Appl. 376 (2011), pp. 528–534.
- Y. Niu, The large deviations theorem and sensitivity, Chaos Solitons Fractals 42 (2009), pp. 609–614.
- Y. Niu and S. Su, On strong ergodicity and chaoticity of systems with the asymptotic average shadowing property, Chaos Solitons Fractals 44 (2011), pp. 429–432.
- Y. Niu, S. Su, and and B. Zhou, Strong sensitivity of systems satisfying the large deviations theorem, Int. J. Gen. Syst. 44 (2015), pp. 98–105.
- Y. Niu, Y. Wang, and S. Su, The asymptotic average shadowing property and strong ergodicity, Chaos Solitons Fractals 53 (2013), pp. 34–38.
- K. Peterson, Ergodic Theory, Cambridge University Press, New York, 1983.
- P. Walters, An Introduction to Ergodic Theory, Springer-Verlag, New York, 1982.
- Y. Wang and Y. Niu, Strong ergodicity of systems with the average shadowing property, Dynam. Sys.-An Int. J. 29 (2014), pp. 18–23.
- H. Wang and J. Xiong, Some properties of topologically ergodic maps, Acta. Math. Sin. 47 (2004), pp. 859–866 ( in Chinese).
- X. Wu and G. Chen, On the large deviations theorem and ergodicity, Commun. Nonlin. Sci. Numer. Simulat. 30 (2016), pp. 243–247.
- J. Xiong and Z. Yang, Chaos caused by a topologically mixing maps, in Dynamical Systems and Related Topics. World Scientific Press, Singapore, 1992.
- R. Yang, Topologically ergodic maps, Acta. Math. Sinica 44 (2001), pp. 1063–1068 ( in Chinese).
- R. Yang, Topological ergodicity and topological double ergodicity, Acta. Math. Sinica 46 (2003), pp. 555–560 ( in Chinese).