Buried points and lakes of Wada Continua

Yeshun Sun; Chung-Chun Yang

doi:10.3934/dcds.2003.9.379

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2003, Volume 9, Issue 2: 379-382. Doi: 10.3934/dcds.2003.9.379

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Buried points and lakes of Wada Continua

Yeshun Sun^1, and
Chung-Chun Yang^2,

1.
Department of Mathematics, Zhejiang University, Hangzhou, Zhejiang 310027
2.
Department of Mathematics, Hang Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received: May 31, 2001

Revised: January 31, 2002

Published: February 2003

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Abstract

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.

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Mathematics Subject Classification: Primary 37F10, 37F50.

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