Abstract
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 Bahabadi (Georgian Math J 22:179–184, 2015).
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06 February 2018
In the original publication of the article, the fund name “Youth Science and Technology Innovation Team of SWPU for Nonlinear Systems (No. 2017CXTD02)” has been missed.
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Acknowledgements
This work was supported by the scientific research starting project of Southwest Petroleum University (No. 2015QHZ029), the Independent Research Foundation of the Central Universities (No. DC 201502050201), and the National Natural Science Foundation of China (No. 11601449, 11271061).
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A correction to this article is available online at https://doi.org/10.1007/s12346-018-0271-6.
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Wu, X., Wang, L. & Liang, J. The Chain Properties and Average Shadowing Property of Iterated Function Systems. Qual. Theory Dyn. Syst. 17, 219–227 (2018). https://doi.org/10.1007/s12346-016-0220-1
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DOI: https://doi.org/10.1007/s12346-016-0220-1