Affine transformations of hyperbolic number plane

Öztürk İ., ÖZDEMİR M.

Boletin de la Sociedad Matematica Mexicana, vol.28, no.3, 2022 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 3
  • Publication Date: 2022
  • Doi Number: 10.1007/s40590-022-00455-2
  • Journal Name: Boletin de la Sociedad Matematica Mexicana
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, DIALNET
  • Keywords: Affine transformation, Fractals, Hyperbolic numbers, Iterated function system, Lorentzian plane
  • Akdeniz University Affiliated: Yes

Abstract

© 2022, Sociedad Matemática Mexicana.Just as the motions in the Euclidean plane can be studied with the help of complex numbers, the motions in the Lorentzian plane can be studied with the help of hyperbolic numbers. The purpose of this article is to determine affine transformations on Lorentzian plane using the set of hyperbolic numbers and to give some examples on hyperbolical fractals. Also, we give some properties of hyperbolical reflections and rotations.