A fixed point theorem for branched covering maps of the plane

Academic Article

Abstract

  • It is known that every homeomorphism of the plane which admits an invariant non-separating continuum has a fixed point in the continuum. In this paper we show that any branched covering map of the plane of degree d, |d| < 2, which has an invariant, non-separating continuum Y, either has a fixed point in Y, or is such that Y contains a minimal (in the sense of inclusion among invariant continua), fully invariant, non-separating subcontinuum X. In the latter case, f has to be of degree -2 and X has exactly three fixed prime ends, one corresponding to an outchannel and the other two to inchannels. © 2009 Instutut Matematyczny PAN.
  • Published In

    Digital Object Identifier (doi)

    Author List

  • Blokh A; Oversteegen L
  • Start Page

  • 77
  • End Page

  • 111
  • Volume

  • 206
  • Issue

  • 1