Abstract
Topological conjugacy between multifunctions plays an important role in the research of dynamical systems. This paper deals with conjugacies of strictly increasing and upper semicontinuous multifunctions on a closed interval with finite set-valued points. All conjugacies between these two multifunctions are constructed with an extension method. The \(C^{1}\) smoothness of the conjugacies is also given. Moreover, an example is presented to illustrate the applications of the main results.
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Acknowledgements
The authors would like to thank the referees for their valuable comments and suggestions. This research is supported by the National Natural Science Foundation of China (No. 11771197), the Guangdong Natural Science Foundation of China (Nos. 2017A030313030 and 2018A0303070012), the Natural Science Foundation of Fujian Province of China (No. 2019J01064), the Scientific Research Funds of Huaqiao University and the KSP of Lingnan Normal University (No. 1171518004).
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Liu, J., Deng, S. Topological conjugacy between multifunctions. Aequat. Math. 93, 1203–1220 (2019). https://doi.org/10.1007/s00010-019-00676-3
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DOI: https://doi.org/10.1007/s00010-019-00676-3