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Contact of fuchsian group with hyperbolic metric.

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Hisoblash va amaliy matematika muammolari

Hisoblash va amaliy matematika muammolari

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ARTICLE ANNOTATION

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The article suggests the study of conditions discreteness free product of finite cyclic groups, also checkisng this condition for which no specific finitely generated groups. The invariance of the hyperbolic metric relative to the action of a Fuchsian group is proved. The examples of the areas in hyperbolic metric are considered. The article contains supporting information about the characteristics of bilinear mappings, transformations of the isometric circles and building with them the fundamental domain Ford for proper discontinuous groups, in particular, for Fuchsian groups. Results of Hering, MacLachlan and Martin are stated. In the results the example of two elliptic transformations is built to verify that they meet the conditions of Goering, MacLachlan and Martin.

AUTHORS

M.Aripov

Национального университета Узбекистана

Y.Yuldoshv

Узбекского Государственного университета мировых языков

Tags

# циклические группы# гиперболическая линия# элементы группы Клейна# дискретные группы Мёбиуса# изометрическая окружность# фундаментальная область# sikl guruhlar# gipеrbolik chiziq# Klеyna gruppasining elеmеntlari# Myobiusa diskrеt gruppasi# izomеtrik aylana# fundamеntal oblast# cyclic groups# a hyperbolic line# elements of Klein group# discrete Mobius groups# isometric circle fundamental reg

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Article Identifiers

ROI:

https://eroi.uz/11.0007/A1119-0049

DOI:

Not Available

References

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