Discrete dynamics of contractions on graphs

Ostapyuk, Olena; Ronnenberg, Mark

doi:10.2140/involve.2017.10.495

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1944-4184 (online)

ISSN 1944-4176 (print)

Author index

To appear

Other MSP journals

Discrete dynamics of contractions on graphs

Olena Ostapyuk and Mark Ronnenberg

Vol. 10 (2017), No. 3, 495–503

DOI: 10.2140/involve.2017.10.495

Abstract

We study the dynamical behavior of functions on vertices of a graph that are contractions in the graph metric. We show that the fixed point set of such functions must be convex. If a function has no fixed points and the graph is a tree, we prove that every dynamical cycle must have an even period and the function behaves eventually like a symmetry.

Keywords

discrete dynamics, dynamics of contractions, graphs

Mathematical Subject Classification 2010

Primary: 39B12, 54H20

Secondary: 05C05

Milestones

Received: 14 February 2016

Revised: 12 April 2016

Accepted: 14 April 2016

Published: 14 December 2016

Communicated by Martin Bohner

Authors

Olena Ostapyuk
Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614-0506 United States

Mark Ronnenberg
Department of Mathematics University of Northern Iowa Cedar Falls, IA 50614-0506 United States

Vol. 10, No. 3, 2017