Conjugacy classification of bicomplex Mobius transformations

被引：0
作者：
Li, Zekun [1 ,2 ]
Dai, Binlin [1 ]
机构：
[1] Shanghai Univ Finance & Econ, Sch Math, Shanghai, Peoples R China
[2] Sun Yat Sen Univ, Sch Math, Guangzhou, Peoples R China
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2024年 / 69卷 / 10期
关键词：
Conjugacy classification; Mobius transformation; fixed points; bicomplex numbers;
D O I：
10.1080/17476933.2023.2241015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the Mobius groups theory in the framework of bicomplex numbers, which are pairs of complex numbers making up a commutative ring with zero-divisors. In this paper, we first generalize classical conjugacy classification to bicomplex analysis. Then we have a discussion of the iterates of a bicomplex Mobius transformation and study the attractive and repulsive fixed points in bicomplex setting. Finally, we shall prove two useful results concerning fixed point.
引用
收藏
页码：1663 / 1678
页数：16
相关论文
共 22 条
  • [1] ON THE FIXED-POINTS OF MOBIUS TRANSFORMATIONS IN RN
    AHLFORS, LV
    [J]. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 1985, 10 (01): : 15 - 27
  • [2] Alpay D, 2014, SPRINGERBRIEF MATH, P1, DOI 10.1007/978-3-319-05110-9
  • [3] Beardon A.F., 1983, GRADUATE TEXTS MATH, V91, pxii+337, DOI 10.1007/978-1-4612-1146-4
  • [4] On bicomplex third-order Jacobsthal numbers
    Cerda-Morales, Gamaliel
    [J]. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2023, 68 (01) : 44 - 56
  • [5] The Fixed Points and Cross-Ratios of Hyperbolic Mobius Transformations in Bicomplex Space
    Chen, Litao
    Dai, Binlin
    [J]. ADVANCES IN APPLIED CLIFFORD ALGEBRAS, 2022, 32 (04)
  • [6] Dai B., 2002, COMPLEX VAR, V47, P149, DOI [10.1080/02781070290010896, DOI 10.1080/02781070290010896]
  • [7] Emanuello J. A., 2015, Analysis of functions of split-complex, multicomplex and split-quaternionic variables and their associated conformal geometries
  • [8] Emanuello JA, 2015, COMPLEX ANAL OPER TH, V9, P329, DOI 10.1007/s11785-014-0363-5
  • [9] Conjugacy invariants of Sl(2, H)
    Foreman, B
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 381 : 25 - 35
  • [10] Ghosh C., 2017, ARXIV
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