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On the Dynamic Geometry of Kasner Polygons with Complex Parameter

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Difference Equations, Discrete Dynamical Systems and Applications (ICDEA 2022)

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Abstract

In this paper we explore the dynamics of the sequence of Kasner polygons \((A^1_nA^2_n\dots A^k_n)_{n\ge 0}\) situated in the plane, defined for a complex parameter \(\alpha \), and find the parameter values ensuring that the iterations are convergent, periodic or divergent. The results generalize and extend previous research on Kasner triangles and quadrilaterals with a fixed real parameter, where it was found that iterations were convergent if and only if \(0< \alpha < 1\), that is polygons in the sequence are nested.

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Author information

Authors and Affiliations

  1. Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Dorin Andrica

  2. University of Derby, Kedleston Road, Derby, DE22 1GB, UK

    Ovidiu Bagdasar

  3. “1 Decembrie 1918” University of Alba Iulia, 510009, Alba Iulia, Romania

    Ovidiu Bagdasar

Authors
  1. Dorin Andrica
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  2. Ovidiu Bagdasar
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Correspondence to Ovidiu Bagdasar .

Editor information

Editors and Affiliations

  1. CentraleSupélec, Gif-sur-Yvette, France

    Sorin Olaru

  2. University of Arizona, Tucson, AZ, USA

    Jim Cushing

  3. Trinity University, San Antonio, TX, USA

    Saber Elaydi

  4. University Côte d’Azur, Nice, Parc Valrose, Cedex 2, France

    René Lozi

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Andrica, D., Bagdasar, O. (2024). On the Dynamic Geometry of Kasner Polygons with Complex Parameter. In: Olaru, S., Cushing, J., Elaydi, S., Lozi, R. (eds) Difference Equations, Discrete Dynamical Systems and Applications. ICDEA 2022. Springer Proceedings in Mathematics & Statistics, vol 444. Springer, Cham. https://doi.org/10.1007/978-3-031-51049-6_4

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