Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Homotopy minimal periods for expanding maps on infra-nilmanifolds
Jong Bum LeeXuezhi Zhao
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2007 Volume 59 Issue 1 Pages 179-184

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Abstract
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 m0, which depends only on n, such that for any integer mm0, 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, [m0,∞)⊂HPer(f). This extends the main result, Theorem 4.6, of [13] from periods to homotopy periods.
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© 2007 The Mathematical Society of Japan
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