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A Topological Classification of Interval Mappings with Finitely Many Discontinuous Points

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Abstract

Topological conjugacy plays an important role in the study of dynamical systems and functional equations. In this paper, a topological classification for monotone functions with finitely many discontinuous points is considered. By introducing the definition of symbolic vector for discontinuous functions, we present necessary and sufficient conditions to determine the conjugate relations between these functions. Moreover, the explicit expressions for those conjugacies are also given. Finally, as an application, our results are applied to the study of classification of generalized Lorenz maps.

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Acknowledgements

The authors are very grateful to the reviewers for their carefully checking and helpful suggestions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, Guangdong, People’s Republic of China

    Jinghua Liu

  2. College of Data Science, Jiaxing University, Jiaxing, 314001, Zhejiang, People’s Republic of China

    Lin Li

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  1. Jinghua Liu
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  2. Lin Li
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Correspondence to Lin Li.

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This work is supported by the National Science Foundation of China (#12026207, #11701476) and Natural Science Foundation of Guangdong Province (#2022A1515010964).

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Liu, J., Li, L. A Topological Classification of Interval Mappings with Finitely Many Discontinuous Points. Qual. Theory Dyn. Syst. 21, 157 (2022). https://doi.org/10.1007/s12346-022-00686-8

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