Buried Sierpinski curve Julia sets

Previous Article
Robustness of asymptotic stability to small time delays
DCDS Home
This Issue
Next Article
Periodic points of holomorphic twist maps

July 2005, 13(4): 1035-1046. doi: 10.3934/dcds.2005.13.1035

Buried Sierpinski curve Julia sets

Robert L. Devaney ^1, and Daniel M. Look ^1,

1.	Department of Mathematics, Boston University, Boston, MA 02215, United States, United States

Received September 2004 Revised March 2005 Published August 2005

Abstract
Related Papers

In this paper we prove the existence of a new type of Sierpinski curve Julia set for certain families of rational maps of the complex plane. In these families, the complementary domains consist of open sets that are preimages of the basin at $\infty$ as well as preimages of other basins of attracting cycles.

Keywords: Julia sets, rational map., Sierpinski curve.

Mathematics Subject Classification: Primary: 37F45; Secondary: 37F2.

Citation: Robert L. Devaney, Daniel M. Look. Buried Sierpinski curve Julia sets. Discrete & Continuous Dynamical Systems - A, 2005, 13 (4) : 1035-1046. doi: 10.3934/dcds.2005.13.1035

[1]	Weiyuan Qiu, Fei Yang, Yongcheng Yin. Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps. Discrete & Continuous Dynamical Systems - A, 2016, 36 (6) : 3375-3416. doi: 10.3934/dcds.2016.36.3375
[2]	Rich Stankewitz, Hiroki Sumi. Random backward iteration algorithm for Julia sets of rational semigroups. Discrete & Continuous Dynamical Systems - A, 2015, 35 (5) : 2165-2175. doi: 10.3934/dcds.2015.35.2165
[3]	Hiroki Sumi, Mariusz Urbański. Measures and dimensions of Julia sets of semi-hyperbolic rational semigroups. Discrete & Continuous Dynamical Systems - A, 2011, 30 (1) : 313-363. doi: 10.3934/dcds.2011.30.313
[4]	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 & Continuous Dynamical Systems - A, 2019, 39 (9) : 5185-5206. doi: 10.3934/dcds.2019211
[5]	Jun Hu, Oleg Muzician, Yingqing Xiao. Dynamics of regularly ramified rational maps: Ⅰ. Julia sets of maps in one-parameter families. Discrete & Continuous Dynamical Systems - A, 2018, 38 (7) : 3189-3221. doi: 10.3934/dcds.2018139
[6]	Koh Katagata. Quartic Julia sets including any two copies of quadratic Julia sets. Discrete & Continuous Dynamical Systems - A, 2016, 36 (4) : 2103-2112. doi: 10.3934/dcds.2016.36.2103
[7]	Luiz Henrique de Figueiredo, Diego Nehab, Jorge Stolfi, João Batista S. de Oliveira. Rigorous bounds for polynomial Julia sets. Journal of Computational Dynamics, 2016, 3 (2) : 113-137. doi: 10.3934/jcd.2016006
[8]	Danilo Antonio Caprio. A class of adding machines and Julia sets. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 5951-5970. doi: 10.3934/dcds.2016061
[9]	Nathaniel D. Emerson. Dynamics of polynomials with disconnected Julia sets. Discrete & Continuous Dynamical Systems - A, 2003, 9 (4) : 801-834. doi: 10.3934/dcds.2003.9.801
[10]	Sebastián Ferrer, Francisco Crespo. Alternative angle-based approach to the $\mathcal{KS}$-Map. An interpretation through symmetry and reduction. Journal of Geometric Mechanics, 2018, 10 (3) : 359-372. doi: 10.3934/jgm.2018013
[11]	Rich Stankewitz. Density of repelling fixed points in the Julia set of a rational or entire semigroup, II. Discrete & Continuous Dynamical Systems - A, 2012, 32 (7) : 2583-2589. doi: 10.3934/dcds.2012.32.2583
[12]	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
[13]	Tarik Aougab, Stella Chuyue Dong, Robert S. Strichartz. Laplacians on a family of quadratic Julia sets II. Communications on Pure & Applied Analysis, 2013, 12 (1) : 1-58. doi: 10.3934/cpaa.2013.12.1
[14]	Krzysztof Barański, Michał Wardal. On the Hausdorff dimension of the Sierpiński Julia sets. Discrete & Continuous Dynamical Systems - A, 2015, 35 (8) : 3293-3313. doi: 10.3934/dcds.2015.35.3293
[15]	Ali Messaoudi, Rafael Asmat Uceda. Stochastic adding machine and $2$-dimensional Julia sets. Discrete & Continuous Dynamical Systems - A, 2014, 34 (12) : 5247-5269. doi: 10.3934/dcds.2014.34.5247
[16]	Ranjit Bhattacharjee, Robert L. Devaney, R.E. Lee Deville, Krešimir Josić, Monica Moreno-Rocha. Accessible points in the Julia sets of stable exponentials. Discrete & Continuous Dynamical Systems - B, 2001, 1 (3) : 299-318. doi: 10.3934/dcdsb.2001.1.299
[17]	Marie-Claude Arnaud. A nondifferentiable essential irrational invariant curve for a $C^1$ symplectic twist map. Journal of Modern Dynamics, 2011, 5 (3) : 583-591. doi: 10.3934/jmd.2011.5.583
[18]	Koh Katagata. Transcendental entire functions whose Julia sets contain any infinite collection of quasiconformal copies of quadratic Julia sets. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 5319-5337. doi: 10.3934/dcds.2019217
[19]	Rich Stankewitz, Hiroki Sumi. Backward iteration algorithms for Julia sets of Möbius semigroups. Discrete & Continuous Dynamical Systems - A, 2016, 36 (11) : 6475-6485. doi: 10.3934/dcds.2016079
[20]	Alexander Blokh, Lex Oversteegen, Vladlen Timorin. Non-degenerate locally connected models for plane continua and Julia sets. Discrete & Continuous Dynamical Systems - A, 2017, 37 (11) : 5781-5795. doi: 10.3934/dcds.2017251

2018 Impact Factor: 1.143

American Institute of Mathematical Sciences