Möbius Transformations in the Second Symmetric Product of ℂ

Gabriela Hinojosa, Ulises Morales-Fuentes and Rogelio Valdez ()
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Gabriela Hinojosa: Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca 62209, Morelos, Mexico
Ulises Morales-Fuentes: Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca 62209, Morelos, Mexico
Rogelio Valdez: Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma del Estado de Morelos, Cuernavaca 62209, Morelos, Mexico

Mathematics, 2025, vol. 13, issue 5, 1-19

Abstract: Let F 2 ( C ) denote the second symmetric product of the complex plane C endowed with the Hausdorff topology, i.e., F 2 ( C ) = { A ⊂ C : | A | ≤ 2 , A ≠ ∅ } . In this paper, we extended the concept of Möbius transformations to F 2 ( C ) . More precisely, given a Möbius transformation T of C , we define the map T ˜ ( { z , w } ) = { T ( z ) , T ( w ) } within F 2 ( C ) . We describe some general properties of these maps, including the structure of their generators, characteristics related to transitivity, and the geometry of the conjugacy classes.

Keywords: second symmetric product; Möbius transformations; transitivity; conjugacy classes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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