The chain properties and average shadowing property of iterated function systems. (English) Zbl 1392.37009
Qual. Theory Dyn. Syst. 17, No. 1, 219-227 (2018); erratum ibid. 17, No. 1, 229 (2018).
Summary: This note proves that an iterated function system is chain transitive (resp., chain mixing, transitive) if and only if the step skew product corresponding to the iterated function system is chain transitive (resp., chain mixing, transitive). As an application, it is obtained that an iterated function system with the (asymptotic) average shadowing property is chain mixing, improving the main results in [A. Z. Bahabadi, Georgian Math. J. 22, No. 2, 179–184 (2015; Zbl 1371.37013)].
MSC:
| 37B05 | Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) |
| 54H20 | Topological dynamics (MSC2010) |
| 37B20 | Notions of recurrence and recurrent behavior in topological dynamical systems |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 37C50 | Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics |
Citations:
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