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January, 2007 Homotopy minimal periods for expanding maps on infra-nilmanifolds
Jong Bum LEE, Xuezhi ZHAO
J. Math. Soc. Japan 59(1): 179-184 (January, 2007). DOI: 10.2969/jmsj/1180135506


We prove that the sets of homotopy minimal periods for expanding maps on n -dimensional infra-nilmanifolds are uniformly cofinite,i.e., there exists a positive integer m 0 , which depends only on n , such that for any integer m m 0 , for any n -dimensional infra-nilmanifold M , and for any expanding map f on M , any self-map on M homotopic to f has a periodic point of least period m , namely, [ m 0 , ) H P e r ( f ) . This extends the main result, Theorem 4.6, of [13] from periods to homotopy periods.


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Jong Bum LEE. Xuezhi ZHAO. "Homotopy minimal periods for expanding maps on infra-nilmanifolds." J. Math. Soc. Japan 59 (1) 179 - 184, January, 2007.


Published: January, 2007
First available in Project Euclid: 25 May 2007

zbMATH: 1119.55002
MathSciNet: MR2302668
Digital Object Identifier: 10.2969/jmsj/1180135506

Primary: ‎55M20
Secondary: 57S30

Keywords: essentially reducible , expanding maps , homotopy minimal periods , Infra-nilmanifolds

Rights: Copyright © 2007 Mathematical Society of Japan


Vol.59 • No. 1 • January, 2007
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