Vol. 83, No. 1, 1979

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Periodic points on tori

Benjamin Rigler Halpern

Vol. 83 (1979), No. 1, 117–133
Abstract

We prove the following theorem.

Theorem 1. Given a continuous map f : Tn Tn of the n-dimensional torus into itself. Each map homotopic to f has an infinite number of periodic points if and only if the Lefschetz numbers of the iterates L(fm), m = 1,2,, are unbounded.

Mathematical Subject Classification 2000
Primary: 55M20
Secondary: 54H25, 58F20
Milestones
Received: 15 February 1978
Revised: 4 December 1978
Published: 1 July 1979
Authors
Benjamin Rigler Halpern