Expanding maps on infra-nilmanifolds of homogeneous type

Authors:
Karel Dekimpe and Kyung Bai Lee

Journal:
Trans. Amer. Math. Soc. **355** (2003), 1067-1077

MSC (2000):
Primary 37D20; Secondary 17B30, 17B70

DOI:
https://doi.org/10.1090/S0002-9947-02-03084-2

Published electronically:
October 24, 2002

MathSciNet review:
1938746

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we investigate expanding maps on infra-nilmanifolds. Such manifolds are obtained as a quotient , where is a connected and simply connected nilpotent Lie group and is a torsion-free uniform discrete subgroup of , with a compact subgroup of . We show that if the Lie algebra of is homogeneous (i.e., graded and generated by elements of degree 1), then the corresponding infra-nilmanifolds admit an expanding map. This is a generalization of the result of H. Lee and K. B. Lee, who treated the 2-step nilpotent case.

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Additional Information

**Karel Dekimpe**

Affiliation:
Katholieke Universiteit Leuven Campus Kortrijk, Universitaire Campus, B-8500 Kortrijk, Belgium

Email:
Karel.Dekimpe@kulak.ac.be

**Kyung Bai Lee**

Affiliation:
University of Oklahoma, Norman, Oklahoma 73019

Email:
kblee@math.ou.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-03084-2

Keywords:
Infra-nilmanifold,
expanding map,
homogeneous Lie group

Received by editor(s):
December 11, 2000

Received by editor(s) in revised form:
March 15, 2002

Published electronically:
October 24, 2002

Article copyright:
© Copyright 2002
American Mathematical Society