Acknowledgement
The author was supported by grant agreement No.SCU. MM1400.418 from SCU (Shahid Chamran University of Ahvaz) in Iran.
References
- S. A. Ahmadi and M. R. Molaei, Exponential limit shadowing, Ann. Polon. Math. 108 (2013), no. 1, 1-10. https://doi.org/10.4064/ap108-1-1
- E. Akin, M. Hurley, and J. A. Kennedy, Dynamics of topologically generic homeomorphisms, Mem. Amer. Math. Soc. 164 (2003), no. 783, viii+130 pp. https://doi.org/10.1090/memo/0783
- B. Carvalho and D. Kwietniak, On homeomorphisms with the two-sided limit shadowing property, J. Math. Anal. Appl. 420 (2014), no. 1, 801-813. https://doi.org/10.1016/j.jmaa.2014.06.011
- T. Eirola, O. Nevanlinna, and S. Yu. Pilyugin, Limit shadowing property, Numer. Funct. Anal. Optim. 18 (1997), no. 1-2, 75-92. https://doi.org/10.1080/01630569708816748
- R. Gu, The asymptotic average shadowing property and transitivity, Nonlinear Anal. 67 (2007), no. 6, 1680-1689. https://doi.org/10.1016/j.na.2006.07.040
- M. Kulczycki, D. Kwietniak, and P. Oprocha, On almost specification and average shadowing properties, Fund. Math. 224 (2014), no. 3, 241-278. https://doi.org/10.4064/fm224-3-4
- K. Lee and K. Sakai, Various shadowing properties and their equivalence, Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 533-540. https://doi.org/10.3934/dcds.2005.13.533
- K. Palmer, Shadowing in dynamical systems, Mathematics and its Applications, 501, Kluwer Academic Publishers, Dordrecht, 2000. https://doi.org/10.1007/978-1-4757-3210-8
- S. Yu. Pilyugin, Shadowing in dynamical systems, Lecture Notes in Mathematics, 1706, Springer-Verlag, Berlin, 1999.
- S. Yu. Pilyugin, Sets of dynamical systems with various limit shadowing properties, J. Dynam. Differential Equations 19 (2007), no. 3, 747-775. https://doi.org/10.1007/s10884-007-9073-2
- S. Yu. Pilyugin and S. Tikhomirov, Lipschitz shadowing implies structural stability, Nonlinearity 23 (2010), no. 10, 2509-2515. https://doi.org/10.1088/0951-7715/23/10/009
- O. B. Plamenevskaya, Weak shadowing for two-dimensional diffeomorphisms, Mat. Zametki 65 (1999), 477-480.
- K. Sakai, Shadowing properties of L-hyperbolic homeomorphisms, Topology Appl. 112 (2001), no. 3, 229-243. https://doi.org/10.1016/S0166-8641(00)00002-X
- K. Sakai, Various shadowing properties for positively expansive maps, Topology Appl. 131 (2003), no. 1, 15-31. https://doi.org/10.1016/S0166-8641(02)00260-2