ISSN:
1420-8946
Keywords:
Key words. Foliated metric space, generic, residual, meager, endset, totally recurrent leaf.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. A remarkable theorem of E. Ghys asserts that, for any harmonic measure $ \mu $ on a compact, foliated metric space, $ \mu $ -almost every leaf has 0, 1, 2 or a Cantor set of ends. In this paper, analogous results are proven for topologically almost all (i.e., residual families of) leaves. More precisely, if some leaf is totally recurrent, a residual family of leaves is totally recurrent with 1, 2 or a Cantor set of ends. A "local" version of this theorem asserts that, in general, topologically almost all leaves have 0, 1, 2 or a Cantor set of dense ends.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000140050057
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