# American Institute of Mathematical Sciences

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

## Buried points and lakes of Wada Continua

 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.
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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