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Regular version of the site

Article

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

Discrete and Continuous Dynamical Systems. 2017. Vol. 37. No. 11. P. 5781-5795.
Blokh A., Oversteegen L., Timorin V.

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.