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Generalisation of the Mandelbrot set to integral functions of quaternions
1. | Department of Mathematics, Glasgow Caledonian University, Glasgow, United Kingdom, United Kingdom |
[1] |
Koh Katagata. Quartic Julia sets including any two copies of quadratic Julia sets. Discrete and Continuous Dynamical Systems, 2016, 36 (4) : 2103-2112. doi: 10.3934/dcds.2016.36.2103 |
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Tarik Aougab, Stella Chuyue Dong, Robert S. Strichartz. Laplacians on a family of quadratic Julia sets II. Communications on Pure and Applied Analysis, 2013, 12 (1) : 1-58. doi: 10.3934/cpaa.2013.12.1 |
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Héctor A. Tabares-Ospina, Mauricio Osorio. Methodology for the characterization of the electrical power demand curve, by means of fractal orbit diagrams on the complex plane of Mandelbrot set. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1895-1905. doi: 10.3934/dcdsb.2020008 |
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Koh Katagata. Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of quadratic Julia sets. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5319-5337. doi: 10.3934/dcds.2019217 |
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Robert L. Devaney, Daniel M. Look. Buried Sierpinski curve Julia sets. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 1035-1046. doi: 10.3934/dcds.2005.13.1035 |
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Danilo Antonio Caprio. A class of adding machines and Julia sets. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 5951-5970. doi: 10.3934/dcds.2016061 |
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Nathaniel D. Emerson. Dynamics of polynomials with disconnected Julia sets. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 801-834. doi: 10.3934/dcds.2003.9.801 |
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Igor E. Pritsker and Richard S. Varga. Weighted polynomial approximation in the complex plane. Electronic Research Announcements, 1997, 3: 38-44. |
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Tien-Cuong Dinh, Nessim Sibony. Rigidity of Julia sets for Hénon type maps. Journal of Modern Dynamics, 2014, 8 (3&4) : 499-548. doi: 10.3934/jmd.2014.8.499 |
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Krzysztof Barański, Michał Wardal. On the Hausdorff dimension of the Sierpiński Julia sets. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3293-3313. doi: 10.3934/dcds.2015.35.3293 |
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Ali Messaoudi, Rafael Asmat Uceda. Stochastic adding machine and $2$-dimensional Julia sets. Discrete and Continuous Dynamical Systems, 2014, 34 (12) : 5247-5269. doi: 10.3934/dcds.2014.34.5247 |
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Ranjit Bhattacharjee, Robert L. Devaney, R.E. Lee Deville, Krešimir Josić, Monica Moreno-Rocha. Accessible points in the Julia sets of stable exponentials. Discrete and Continuous Dynamical Systems - B, 2001, 1 (3) : 299-318. doi: 10.3934/dcdsb.2001.1.299 |
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Weiyuan Qiu, Fei Yang, Yongcheng Yin. Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 3375-3416. doi: 10.3934/dcds.2016.36.3375 |
[18] |
Rich Stankewitz, Hiroki Sumi. Random backward iteration algorithm for Julia sets of rational semigroups. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 2165-2175. doi: 10.3934/dcds.2015.35.2165 |
[19] |
Rich Stankewitz, Hiroki Sumi. Backward iteration algorithms for Julia sets of Möbius semigroups. Discrete and Continuous Dynamical Systems, 2016, 36 (11) : 6475-6485. doi: 10.3934/dcds.2016079 |
[20] |
Youming Wang, Fei Yang, Song Zhang, Liangwen Liao. Escape quartered theorem and the connectivity of the Julia sets of a family of rational maps. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 5185-5206. doi: 10.3934/dcds.2019211 |
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