Nonexponential leaves at finite level

Cantwell, John; Conlon, Lawrence

doi:10.1090/S0002-9947-1982-0637715-X

Nonexponential leaves at finite level
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by John Cantwell and Lawrence Conlon

Trans. Amer. Math. Soc. 269 (1982), 637-661

DOI: https://doi.org/10.1090/S0002-9947-1982-0637715-X

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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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