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ON v-DISTAL FLOWS ON 3-MANIFOLDS

Published online by Cambridge University Press:  01 September 1997

S. MATSUMOTO  and
H. NAKAYAMA
S. MATSUMOTO
Affiliation:
Department of Mathematics, College of Science and Technology, Nihon University, 1-8 Kanda-Surugadai, Chiyoda-ku, Tokyo 101, Japan
H. NAKAYAMA
Affiliation:
Faculty of Integrated Arts and Sciences, Hiroshima University, 1-7-1, Kagamiyama, Higashi-Hiroshima 739, Japan
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Abstract

In [2], H. Furstenberg studied a distal action of a locally compact group G on a compact metric space X, and established a structure theorem. As a consequence, he showed that if G is abelian, then a simply connected space X does not admit a minimal distal G-action.

In this paper we concern ourselves with a nonsingular flow ϕ={ϕt} on a closed 3-manifold M. Recall that ϕ is called distal if for any distinct two points x, y ∈ M, the distance d(ϕtx, ϕty) is bounded away from 0. The distality depends strongly upon the time parametrization. For example, there exists a time parametrization of a linear irrational flow on T2 which yields a nondistal flow [4, 6].

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 5 , September 1997 , pp. 609 - 616
Copyright
© The London Mathematical Society 1997

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