The Boundedness Locus and Baby Mandelbrot Sets for Some Generalized McMullen Maps

被引：0
|
作者：
Boyd, Suzanne [1 ]
Mitchell, Alexander J. [2 ]
机构：
[1] Univ Wisconsin Milwaukee, Dept Math Sci, POB 413, Milwaukee, WI 53201 USA
[2] Wayne State Coll, Dept Phys Sci & Math, 1111 Main St, Wayne, NE 68787 USA
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2023年 / 33卷 / 09期
关键词：
Complex dynamical system; Mandelbrot set; polynomial-like map; rational map; iteration; JULIA SETS; DYNAMICS; FAMILIES; HALOS;
D O I：
10.1142/S0218127423501079
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we study rational functions of the form R-n,R-a,R-c(z) = z(n) + a/z(n) + c, with n fixed and at least 3, and hold either a or c fixed while the other varies. We locate some homeomorphic copies of the Mandelbrot set in the c-parameter plane for certain ranges of a, as well as in the a-plane for some c-ranges.We use techniques first introduced by Douady and Hubbard [1985] that were applied for the subfamily R-n,R-a,R-0 by Devaney [2006]. These techniques involve polynomial-like maps of degree two.
引用
下载
收藏
页数：23
相关论文
共 50 条
  • [41] Some results on generalized difference sets
    Cao, Xiwang
    JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY, 2008, 21 (01) : 76 - 84
  • [42] Some Results on Generalized Difference Sets
    Xiwang Cao
    Journal of Systems Science and Complexity, 2008, 21 : 76 - 84
  • [43] SOME RESULTS ON GENERALIZED DIFFERENCE SETS
    Xiwang CAO School of Mathematical Science
    State Key Lab. of Information Security
    Journal of Systems Science & Complexity, 2008, (01) : 76 - 84
  • [44] Some properties of generalized rough sets
    Ali, Muhammad Irfan
    Davvaz, B.
    Shabir, Muhammad
    INFORMATION SCIENCES, 2013, 224 : 170 - 179
  • [45] SOME RESULTS ON GENERALIZED DIFFERENCE SETS
    Xiwang CAO School of Mathematical Science Nanjing University of Aeronautics and Astronautics Nanjing China
    State Key Lab of Information Security Beijing China
    JournalofSystemsScienceandComplexity, 2008, 21 (01) : 76 - 84
  • [46] Some Properties of Generalized (∧, α)-Closed Sets
    Boonpok, Chawalit
    Thongmoon, Montri
    INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2023, 21
  • [47] On some maps concerning gα-open sets
    Caldas, M.
    Jafari, S.
    Saraf, R. K.
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2007, 30 (02) : 93 - 98
  • [48] Comparative Study of Some Fixed-Point Methods in the Generation of Julia and Mandelbrot Sets
    Zhou, Hao
    Tanveer, Muhammad
    Li, Jingjng
    JOURNAL OF MATHEMATICS, 2020, 2020
  • [49] Researches on some internal structures of the general Mandelbrot sets for negative real index number
    Wang, X.-Y.
    Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao/Journal of Computer-Aided Design and Computer Graphics, 2001, 13 (10): : 868 - 872
  • [50] Lp BOUNDEDNESS OF THE BERGMAN PROJECTION ON SOME GENERALIZED HARTOGS TRIANGLES
    Beberok, T.
    BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2017, 43 (07) : 2275 - 2280
12345