American Institute of Mathematical Sciences

Advanced
March  2003, 9(2): 379-382. doi: 10.3934/dcds.2003.9.379

Buried points and lakes of Wada Continua

Yeshun Sun 1, and  Chung-Chun Yang 2,

1. 

Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027, China
2. 

Department of Mathematics, Hang Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

Received  June 2001 Revised  February 2002 Published  December 2002

Let $f:\hat \mathbf C\rightarrow \hat \mathbf C$ be a rational map of degree $n\geq 3$ and with exactly two critical points. Assume that the Julia set $J(f)$ is a proper subcontinuum of $\hat \mathbf C$ and there is no completely invariant Fatou component under the iterates $f^{2}$. It is shown that if there is no buried points in $J(f)$, then the Julia set $J(f)$ is a Lakes of Wada continuum, and hence is either an indecomposable continuum or the union of two indecomposable continua.
Keywords: bicritical rational function., Buried point, completely invariant Fatou component, lakes of Wada continuum.
Mathematics Subject Classification: Primary 37F10, 37F5.
Citation: Yeshun Sun, Chung-Chun Yang. Buried points and lakes of Wada Continua. Discrete & Continuous Dynamical Systems, 2003, 9 (2) : 379-382. doi: 10.3934/dcds.2003.9.379
[1]

Jon Aaronson, Michael Bromberg, Nishant Chandgotia. Rational ergodicity of step function skew products. Journal of Modern Dynamics, 2018, 13: 1-42. doi: 10.3934/jmd.2018012
[2]

Alexandre Wagemakers, Alvar Daza, Miguel A. F. Sanjuán. How to detect Wada basins. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 717-739. doi: 10.3934/dcdsb.2020330
[3]

Jingxian Sun, Shouchuan Hu. Flow-invariant sets and critical point theory. Discrete & Continuous Dynamical Systems, 2003, 9 (2) : 483-496. doi: 10.3934/dcds.2003.9.483
[4]

Janina Kotus, Mariusz Urbański. The dynamics and geometry of the Fatou functions. Discrete & Continuous Dynamical Systems, 2005, 13 (2) : 291-338. doi: 10.3934/dcds.2005.13.291
[5]

Jane Hawkins, Michael Taylor. The maximal entropy measure of Fatou boundaries. Discrete & Continuous Dynamical Systems, 2018, 38 (9) : 4421-4431. doi: 10.3934/dcds.2018192
[6]

Hans Koch. A renormalization group fixed point associated with the breakup of golden invariant tori. Discrete & Continuous Dynamical Systems, 2004, 11 (4) : 881-909. doi: 10.3934/dcds.2004.11.881
[7]

Qiaoyi Hu, Zhijun Qiao. Analyticity, Gevrey regularity and unique continuation for an integrable multi-component peakon system with an arbitrary polynomial function. Discrete & Continuous Dynamical Systems, 2016, 36 (12) : 6975-7000. doi: 10.3934/dcds.2016103
[8]

Zeng Zhang, Zhaoyang Yin. Global existence for a two-component Camassa-Holm system with an arbitrary smooth function. Discrete & Continuous Dynamical Systems, 2018, 38 (11) : 5523-5536. doi: 10.3934/dcds.2018243
[9]

Nejib Mahmoudi. Single-point blow-up for a multi-component reaction-diffusion system. Discrete & Continuous Dynamical Systems, 2018, 38 (1) : 209-230. doi: 10.3934/dcds.2018010
[10]

Robert L. Devaney, Daniel M. Look. Buried Sierpinski curve Julia sets. Discrete & Continuous Dynamical Systems, 2005, 13 (4) : 1035-1046. doi: 10.3934/dcds.2005.13.1035
[11]

Francesco Mainardi. On some properties of the Mittag-Leffler function $\mathbf{E_\alpha(-t^\alpha)}$, completely monotone for $\mathbf{t> 0}$ with $\mathbf{0<\alpha<1}$. Discrete & Continuous Dynamical Systems - B, 2014, 19 (7) : 2267-2278. doi: 10.3934/dcdsb.2014.19.2267
[12]

Canela Jordi. Singular perturbations of Blaschke products and connectivity of Fatou components. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 3567-3585. doi: 10.3934/dcds.2017153
[13]

Jeremiah Birrell. A posteriori error bounds for two point boundary value problems: A green's function approach. Journal of Computational Dynamics, 2015, 2 (2) : 143-164. doi: 10.3934/jcd.2015001
[14]

Yu-Lin Chang, Jein-Shan Chen, Jia Wu. Proximal point algorithm for nonlinear complementarity problem based on the generalized Fischer-Burmeister merit function. Journal of Industrial & Management Optimization, 2013, 9 (1) : 153-169. doi: 10.3934/jimo.2013.9.153
[15]

Behrouz Kheirfam. A full Nesterov-Todd step infeasible interior-point algorithm for symmetric optimization based on a specific kernel function. Numerical Algebra, Control & Optimization, 2013, 3 (4) : 601-614. doi: 10.3934/naco.2013.3.601
[16]

Siqi Li, Weiyi Qian. Analysis of complexity of primal-dual interior-point algorithms based on a new kernel function for linear optimization. Numerical Algebra, Control & Optimization, 2015, 5 (1) : 37-46. doi: 10.3934/naco.2015.5.37
[17]

Veysel Fuat Hatipoğlu. A novel model for the contamination of a system of three artificial lakes. Discrete & Continuous Dynamical Systems - S, 2021, 14 (7) : 2261-2272. doi: 10.3934/dcdss.2020176
[18]

Guoqiang Wang, Zhongchen Wu, Zhongtuan Zheng, Xinzhong Cai. Complexity analysis of primal-dual interior-point methods for semidefinite optimization based on a parametric kernel function with a trigonometric barrier term. Numerical Algebra, Control & Optimization, 2015, 5 (2) : 101-113. doi: 10.3934/naco.2015.5.101
[19]

Konstantinos Drakakis, Scott Rickard. On the generalization of the Costas property in the continuum. Advances in Mathematics of Communications, 2008, 2 (2) : 113-130. doi: 10.3934/amc.2008.2.113
[20]

Pankaj Kumar Tiwari, Rajesh Kumar Singh, Subhas Khajanchi, Yun Kang, Arvind Kumar Misra. A mathematical model to restore water quality in urban lakes using Phoslock. Discrete & Continuous Dynamical Systems - B, 2021, 26 (6) : 3143-3175. doi: 10.3934/dcdsb.2020223

2019 Impact Factor: 1.338

Tools

Metrics

  • PDF downloads (61)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences