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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 and Continuous Dynamical Systems, 2003, 9 (2) : 379-382. doi: 10.3934/dcds.2003.9.379
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