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Qualitative theory and expansion growth of transversely piecewise-smooth foliated ${S}^{1}$-bundles

Published online by Cambridge University Press:  17 April 2001

SHINJI EGASHIRA
SHINJI EGASHIRA
Affiliation:
Department of Mathematics, Faculty of Science, Saitama University, 255 Shimo-Okubo Urawa, Saitama, 338, Japan
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Abstract

We study a qualitative theory of compact, transversely piecewise-smooth foliated $S^1$-bundles. We show that it has the same qualitative properties as that of smooth codimension-one foliations on a compact manifold. By the obtained qualitative properties, we can deduce that the expansion growth of this foliation is classified and that the entropy of this foliation is positive if and only if there exists a resilient leaf.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 2 , April 1997 , pp. 331 - 347
Copyright
1997 Cambridge University Press

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