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- W2356449069 abstract "Suppose that a $X$ is an emph{unshielded} plane continuum (i.e., $X$ coincides with the boundary of the unbounded complementary component of $X$). Then there exists a emph{finest monotone} map $m:Xto L$, where $L$ is a locally connected continuum (i.e., $m^{-1}(y)$ is connected for each $yin L$, and any monotone map $varphi:Xto L'$ onto a locally connected continuum is a composition $varphi=varphi'circ m$ where $varphi':Lto L'$ is monotone). Such finest locally connected model $L$ of $X$ is easier to understand because $L$ is locally connected (in particular it can be described by a picture) and represents the finest but still understandable decomposition of $X$ into possibly complicated but pairwise disjoint emph{fibers} (point-preimages) of $m$. However, in some cases (i.e., in case $X$ is indecomposable) $L$ is a singleton. In this paper we provide sufficient conditions for the existence of a non-degenerate model depending on the existence of certain subcontinua of $X$ and apply these results to the connected Julia sets of polynomials." @default.
- W2356449069 created "2016-06-24" @default.
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- W2356449069 date "2016-05-09" @default.
- W2356449069 modified "2023-09-23" @default.
- W2356449069 title "Non-degenerate locally connected models for plane continua and Julia sets" @default.
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- W2356449069 doi "https://doi.org/10.48550/arxiv.1605.02691" @default.
- W2356449069 hasPublicationYear "2016" @default.
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