Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1898940 | Journal of Geometry and Physics | 2011 | 13 Pages |
Abstract
We prove that (1) The Lefschetz number of any continuous map ff on an infra-nilmanifold with holonomy group ΨΨ is L(f)=1|Ψ|∑A∈Ψdet(A∗−f∗)detA∗; (2) The sets of periods for expanding maps on nn-dimensional infra-nilmanifolds are uniformly cofinite, i.e., there is a positive integer m0m0, which depends only on nn, such that for any integer m≥m0m≥m0, for any nn-dimensional infra-nilmanifold MM and for any expanding map ff on MM, there exists a periodic point of ff whose least period is exactly mm. This is a generalization of the main result of [R. Tauraso, Sets of periods for expanding maps on flat manifolds, Monatsh. Math. 128 (1999) 151–157] on flat manifolds to infra-nilmanifolds.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Jong Bum Lee, Kyung Bai Lee,