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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nonexponential leaves at finite level

Authors: John Cantwell and Lawrence Conlon
Journal: Trans. Amer. Math. Soc. 269 (1982), 637-661
MSC: Primary 57R30; Secondary 58F18
MathSciNet review: 637715
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Abstract: Previous examples of leaves with nonexponential and nonpolynomial growth (due to G. Hector) have occurred at infinite level. Here the same growth types are produced at finite level in open, saturated sets of leaves without holonomy. Such sets consist of leaves with only one or two locally dense ends, and it is shown that the exotic growth types only occur in the case of one locally dense end. Finally, $ {C^1}$-foliations are produced with open, saturated sets as above in which the leaves have strictly fractional growth.

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Article copyright: © Copyright 1982 American Mathematical Society