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

Academic Article

Abstract

  • 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.
  • Digital Object Identifier (doi)

    Author List

  • Blokh A; Oversteegen L; Timorin V
  • Start Page

  • 5781
  • End Page

  • 5795
  • Volume

  • 37
  • Issue

  • 11