Article Contents
Article Contents

# Non-degenerate locally connected models for plane continua and Julia sets

• * Corresponding author: Alexander Blokh
The first named author was partially supported by NSF grant DMS-1201450.
The second named author was partially supported by NSF grant DMS-0906316.
The third named author was partially supported by the Russian Academic Excellence Project '5-100'
• Every plane continuum admits a finest locally connected model. The latter is a locally connected continuum onto which the original continuum projects in a monotone fashion. It may so happen that the finest locally connected model is a singleton. For example, this happens if the original continuum is indecomposable. In this paper, we provide sufficient conditions for the existence of a non-degenerate model depending on the existence of subcontinua with certain properties. Applications to complex polynomial dynamics are discussed.

Mathematics Subject Classification: Primary: 37F10, 37F20; Secondary: 37F50, 54C10, 54F15.

 Citation:

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