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Julia sets are Cantor circles and Sierpinski carpets for rational maps | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3937-3948 اصل مقاله (668.05 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6193 | ||
| نویسندگان | ||
| Hassanein Q. Al-Salami* 1؛ Iftichar Al-Shara2 | ||
| 1Department of Biology, College of Sciences, University of Babylon, Iraq | ||
| 2Department of Mathematics, College of Education of Pure Sciences, University of Babylon, Iraq | ||
| تاریخ دریافت: 10 مرداد 1400، تاریخ بازنگری: 13 شهریور 1400، تاریخ پذیرش: 23 مهر 1400 | ||
| چکیده | ||
| In this work, we study the family of complex rational maps which is given by $$Q_{\beta }\left(z\right)=2{\beta }^{1-d}z^d-\frac{z^d(z^{2d}-{\beta }^{d+1})}{z^{2d}-{\beta }^{3d-1}},$$ where $d$ greater than or equal to 2 and $\beta{\in }\mathbb{C}{\backslash }\{0\}$ such that $\beta^{1-d}\ne 1$ and $\beta^{2d-2}\ne 1$. We show that ${J(Q}_\beta$) is a Cantor circle or a Sierpinski carpet or a degenerate Sierpinski carpet, whenever the image of one of the free critical points for $Q_\beta$ is not converge to $0$ or $\infty $. | ||
| کلیدواژه‌ها | ||
| Julia sets؛ Cantor circle؛ Sierpinski carpet؛ degenerate Sierpinski carpet | ||
| مراجع | ||
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[1] H.Q. Al-Salami, I. Al-Shara, Rational maps whose Julia sets are quasi circles, Int. J. Nonlinear Anal. Appl. 12(2) (2021) 2041–2048. [2] A. Beardon, Iteration of Rational Functions, Grad. Texts in Math., vol. 132, Springer-Verlag, New York, 1991. [3] M. Bonk, M. Lyubich and S. Merenkov, Quasisymmetries of Sierpi´nski carpet Julia sets, Adv. Math. 301 (2016) 383–422. [4] R.L. Devaney, D. Look and D. Uminsky, The escape trichotomy for singularly perturbed rational maps, Indiana. Univ. Math. J. 54 (2005) 1621–1634. [5] R.L. Devaney, Singular perturbations of complex polynomials, Bull. Amer. Math. Soc. 50 (2013) 391–429. [6] J. Fu and F. Yang, On the dynamics of a family of singularly perturbed rational maps, J. Math. Anal. Appl. 424 (2015) 104–121. [7] A. Garijo and S. Godillon, On McMullen-like mappings, J. Fractal Geom. 2 (2015) 249–279. [8] A. Garijo, S.M. Marotta and E.D. Russell, Singular perturbations in the quadratic family with multiple poles, J. Difference Equ. Appl. 19 (2013) 124–145. [9] D.M. Look, Singular Perturbations of Complex Polynomials and Circle Inversion Maps, Boston University, Thesis, 2005 [10] C. McMullen, Automorphisms of rational maps, in: Holomorphic functions and moduli I, Math. Sci. Res. Inst. Publ. 10, Springer, 1988. [11] J. Milnor, Dynamics in One Complex Variable, third edition, Princeton Univ. Press, Princeton, 2006. [12] J. Milnor, Geometry and dynamics of quadratic rational maps, Experiment. Math. 2 (1993) 37–83. [13] K. Pilgrim and L. Tan, Rational maps with disconnected Julia sets, Asterisque 261 (2000) 349–383. [14] W. Qiu, X. Wang and Y. Yin, Dynamics of McMullen maps, Adv. Math. 229 (2012) 2525–2577. [15] W. Qiu, F. Yang and J. Zeng, Quasisymmetric geometry of the Carpet Julia sets, Fund. Math. 244 (2019) 73–107. [16] Y. Wang, F. Yang, S. Zhang and L. Liao, Escape quartered theorem and the connectivity of the Julia sets of a family of rational maps, Discrete Contin. Dyn. Syst. 39(9) (2019) 5185–5206. [17] Y. Xiao, W. Qiu and Y. Yin, On the dynamics of generalized McMullen maps, Ergod. Th. Dynam. Syst. 34 (2014) 2093-2112. | ||
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