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The Commutative Property of Reciprocal Transformations and Dimensional Deformations

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Abstract

The paper aims to analyze the commutative property of reciprocal transformations and dimensional deformations using conservation laws. First, a geometric proof of the commutative property of reciprocal transformations is presented, based on the coordinate-free property of the exponential map. Second, it is shown that the deformation algorithm does not always keep the commutative property. Illuminating examples are provided.

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Acknowledgements

The work was supported in part by NSFC under the Grants 12271488, 11975145, 11972291 and 51771083, the Ministry of Science and Technology of China (G2021016032L), and the Natural Science Foundation for Colleges and Universities in Jiangsu Province (17 KJB 110020).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Wen-Xiu Ma

  2. Department of Mathematics, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    Wen-Xiu Ma

  3. Department of Mathematics and Statistics, University of South Florida, Tampa, FL, 33620-5700, USA

    Wen-Xiu Ma

  4. Material Science Innovation and Modelling, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, South Africa

    Wen-Xiu Ma

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  1. Wen-Xiu Ma
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WX wrote the main manuscript text, made the computations, and reviewed the manuscript.

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Correspondence to Wen-Xiu Ma.

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Ma, WX. The Commutative Property of Reciprocal Transformations and Dimensional Deformations. Qual. Theory Dyn. Syst. 23, 2 (2024). https://doi.org/10.1007/s12346-023-00856-2

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