Effluent and noneffluent fixed points on dendrites

Helga Schirmer

Vol. 75 (1978), No. 2, 539–552

DOI: 10.2140/pjm.1978.75.539

Abstract

This paper gives a partial answer to the problem of establishing conditions for the existence of selfmaps of one-dimensional spaces with prescribed fixed points and fixed point indices. Two types of isolated fixed points on dendrites are defined, and called effluent and noneffluent fixed points. They correspond on polyhedral trees to fixed points of minimal or maximal algebraic index, but are characterized by separation properties. Necessary and sufficient conditions are given for the existence of a selfmap of a dendrite which has a prescribed set of effluent and noneffluent fixed points.

Mathematical Subject Classification 2000

Primary: 54H25

Secondary: 54F50

Milestones

Received: 19 January 1977

Revised: 27 May 1977

Published: 1 April 1978