Minimal sets of periods for torus maps via Nielsen numbers

Lluís Alsedà, Stewart Baldwin, Jaume Llibre, Richard Swanson and Wieslaw Szlenk

Vol. 169 (1995), No. 1, 1–32

DOI: 10.2140/pjm.1995.169.1

Abstract

The main results in this paper concern the minimal sets of periods possible in a given homotopy class of torus maps. For maps on the 2-torus, we provide a complete description of these minimal sets. A number of results on higher dimensional tori are also proved; including criteria for every map in a given homotopy class to have all periods, or all but finitely many periods.

Mathematical Subject Classification 2000

Primary: 55M20

Secondary: 54H20, 57S25, 58F20

Milestones

Received: 30 September 1992

Revised: 10 June 1993

Published: 1 May 1995