Generalized Chaos game in an extended hyperbolic plane

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Theoretical and Mathematical Physics Pub Date : 2024-08-26 DOI:10.1134/s0040577924080099

L. N. Romakina, I. V. Ushakov

引用次数: 0

Abstract

We propose and theoretically substantiate an algorithm for conducting a generalized Chaos game with an arbitrary jump on finite convex polygons of the extended hyperbolic plane \(H^2\) whose components in the Cayley–Klein projective model are the Lobachevsky plane and its ideal domain. In particular, the defining identities for a point dividing an elliptic, hyperbolic, or parabolic segment in a given ratio are proved, and formulas for calculating the coordinates of such a point at a canonical frame of the first type are obtained. The results of a generalized Chaos game conducted using the advanced software package pyv are presented.

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扩展双曲面中的广义混沌博弈

摘要我们提出并从理论上证实了在扩展双曲面 \(H^2\)的有限凸多边形上进行任意跳跃的广义混沌博弈的算法，其在 Cayley-Klein 投影模型中的成分是洛巴切夫斯基平面及其理想域。特别是，证明了以给定比例分割椭圆、双曲或抛物线段的点的定义同素异形，并获得了计算第一类典型框架中该点坐标的公式。此外，还介绍了使用高级软件包 pyv 进行广义混沌博弈的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Theoretical and Mathematical Physics 物理-物理：数学物理

CiteScore

1.60

自引率

20.00%

发文量

103

审稿时长

4-8 weeks

期刊介绍： Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.