References
- Aoki, N. and Hiraide, K. Topological theory of dynamical systems, Recent advances, North-Holland Mathematical Library, 52, North-Holland Publishing Co., Amsterdam, 1994.
- Auslander, J. Minimal flows and their extensions, North-Holland Mathematics Studies, 153. North-Holland Publishing Co., Amsterdam, 1998.
- Blanchard, F. Topological chaos: what may this mean? Journal of Difference Equations and Applications, Vol.15, Number 1, 23–46(2009). doi: 10.1080/10236190802385355
- Blank, M. L. Small perturbations of chaotic dynamical systems, Russian Math. Surveys, Vol.44, Number 6, 1–33(1989). doi: 10.1070/RM1989v044n06ABEH002302
- Bowen, R. Equilibrium States and the Ergodic Theory of Axiom A Diffeomorphisms, Springer, NewYork, pp. 68–87, 1975.
- Gu, R. The average-shadowing property and transitivity for continuous flows, Chaos, Solitons and Fractals, Vol. 23, Number 3, 989–995(2005).
- Gu, R. The average-shadowing property and topological ergodicity for flows, Chaos, Solitons and Fractals, Vol.25, Number 2, 387–392(2005). doi: 10.1016/j.chaos.2004.11.046
- Gu, R. The average-shadowing property and topological ergodicity, Comput. Math. Appl. Vol.206, Number 2, 796–800(2007). doi: 10.1016/j.cam.2006.08.025
- Kwietniak, D. and Oprocha, P. A note on the average shadowing property for expansive maps, Topology and it Application, Vol.159, Number 1, 19–27(2012). doi: 10.1016/j.topol.2011.04.016
- [10] Li, T. Y. and Yorke, J. A. Period three implies chaos, Am. Math. Monthly, Vol.82, Number 10, 985–992(1975). doi: 10.2307/2318254
- Niu, Y. X. The average-shadowing property and strong ergodicity, J. Math. Anal. Appl., Vol. 376, Number 2, 528–534(2011). doi: 10.1016/j.jmaa.2010.11.024
- Sakai, K. Diffeomorphisms with the average-shadowing property on two dimensional closed manifold, Rocky Mountain J. Math.,Vol. 30, Number 3, 1–9(2000). doi: 10.1216/rmjm/1021477263
- Sakai, K. Vairous shadowing properties for positively expansive maps, Topology and it Applications,Vol. 131, Number 1, 15–31(2003). doi: 10.1016/S0166-8641(02)00260-2
- [14] Walters, P. On the pseudo-orbit tracing property and its relationship to stability, Lecture Notes in Mathematics, vol.668, Springer, Berlin, pp. 224–231, 1978.
- Yang, R. S. The pseudo-orbit tracing property and chaos, Acta Math. Sinica., Vol.39, Number 3, 382–386 (in Chinese)(1996).
- Yang, R. S. Pseudo-orbit tracing property and completely positive entropy, Acta. Math. Sinica., Vol.42, Number 1, 99–104 (in Chinese)(1999).
- Zhou, L. Yin, J. and Xiu, S. Topological dynamical systems, Science Press, Beijing, 2011.
- Wang, Y. and Niu, Y.X. Strong ergodicity of systems with the average shadowing property, Dyn. Sys. Vol.29, Number 1, 18–23(2014). doi: 10.1080/14689367.2013.835791