Homotopy minimal periods for maps of three dimensional nilmanifolds

Jerzy Jezierski and Wacław Marzantowicz

Vol. 209 (2003), No. 1, 85–101

DOI: 10.2140/pjm.2003.209.85

Abstract

A natural number m is called the homotopy minimal period of a map f : X → X if it is a minimal period for every map g homotopic to f. The set HPer (f) of all minimal homotopy periods is an invariant of the dynamics of f which is the same for a small perturbation of f. In this paper we give a complete description of the sets of homotopy minimal periods of self-maps of nonabelian three dimensional nilmanifold which is a counterpart of the corresponding characterization for three dimensional torus proved by Jiang and Llibre. As a corollary we show that if 2 ∈ HPer (f) then HPer (f) = ℕ for such a map.

Milestones

Received: 12 July 2001

Revised: 3 October 2001

Published: 1 March 2003