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Title: Limit sets of Teichmüller geodesics with minimal nonuniquely ergodic vertical foliation, II
Abstract Given a sequence of curves on a surface, we provide conditions which ensure that (1) the sequence is an infinite quasi-geodesic in the curve complex, (2) the limit in the Gromov boundary is represented by a nonuniquely ergodic ending lamination, and (3) the sequence divides into a finite set of subsequences, each of which projectively converges to one of the ergodic measures on the ending lamination. The conditions are sufficiently robust, allowing us to construct sequences on a closed surface of genus g for which the space of measures has the maximal dimension {3g-3} , for example. We also study the limit sets in the Thurston boundary of Teichmüller geodesic rays defined by quadratic differentials whose vertical foliations are obtained from the constructions mentioned above. We prove that such examples exist for which the limit is a cycle in the 1-skeleton of the simplex of projective classes of measures visiting every vertex.  more » « less
Award ID(s):
1510034
PAR ID:
10250782
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Journal für die reine und angewandte Mathematik (Crelles Journal)
Volume:
2020
Issue:
758
ISSN:
0075-4102
Page Range / eLocation ID:
1 to 66
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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