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Affine transformations of hyperbolic number plane. (English) Zbl 1497.15003

Summary: 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.

MSC:

15A04 Linear transformations, semilinear transformations
28A80 Fractals
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
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