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Diophantine and ergodic foliations on surfaces
Author(s) -
McMullen Curtis T.
Publication year - 2013
Publication title -
journal of topology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.447
H-Index - 31
eISSN - 1753-8424
pISSN - 1753-8416
DOI - 10.1112/jtopol/jts033
Subject(s) - mathematics , ergodic theory , foliation (geology) , ergodicity , diophantine equation , geodesic , pure mathematics , upper and lower bounds , characterization (materials science) , mathematical analysis , statistics , materials science , geochemistry , metamorphic rock , nanotechnology , geology
This paper gives a topological characterization of Diophantine and recurrent laminations on surfaces. It also establishes an upper bound for the number of ergodic components of a measured foliation, in terms of limits of the corresponding geodesic ray inM ¯g , n. Taken together, these results give a new approach to Masur's theorem on unique ergodicity.