Asymptotics of Weil-Petersson geodesics II: bounded geometry and unbounded entropy
نویسندگان
چکیده
We use ending laminations for Weil-Petersson geodesics to establish that bounded geometry is equivalent to bounded combinatorics for WeilPetersson geodesic segments, rays, and lines. Further, a more general notion of non-annular bounded combinatorics, which allows arbitrarily large Dehn-twisting, corresponds to an equivalent condition for Weil-Petersson geodesics. As an application, we show the Weil-Petersson geodesic flow has compact invariant subsets with arbitrarily large topological entropy.
منابع مشابه
Coarse and synthetic Weil-Petersson geometry: quasi-flats, geodesics, and relative hyperbolicity
We analyze the coarse geometry of the Weil-Petersson metric on Teichmüller space, focusing on applications to its synthetic geometry (in particular the behavior of geodesics). We settle the question of the strong relative hyperbolicity of the Weil-Petersson metric via consideration of its coarse quasi-isometric model, the pants graph. We show that in dimension 3 the pants graph is strongly rela...
متن کاملAsymptotics of Weil-Petersson geodesics I: ending laminations, recurrence, and flows
We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric [Br2], these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem 1.1) for the full-measure set of rays that recur to the thick part, and...
متن کامل. G T ] 1 3 N ov 2 00 8 Asymptotics of Weil - Petersson geodesics I : ending laminations , recurrence , and flows
We define an ending lamination for a Weil-Petersson geodesic ray. Despite the lack of a natural visual boundary for the Weil-Petersson metric [Br2], these ending laminations provide an effective boundary theory that encodes much of its asymptotic CAT(0) geometry. In particular, we prove an ending lamination theorem (Theorem 1.1) for the full-measure set of rays that recur to the thick part, and...
متن کاملar X iv : 0 81 2 . 29 41 v 1 [ m at h . G T ] 1 5 D ec 2 00 8 ENTROPY VS VOLUME FOR PSEUDO - ANOSOV MAPS
We will discuss theoretical and experimental results concerning comparison of entropy of pseudo-Anosov maps and volume of their mapping tori. Recent study of Weil-Petersson geometry of the Teichmüller space tells us that they admit linear inequalities for both sides under some bounded geometry condition. We construct a family of pseudo-Anosov maps which violates one side of inequalities under u...
متن کاملClassification of Weil-petersson Isometries
This paper contains two main results. The first is the existence of an equivariant Weil-Petersson geodesic in Teichmüller space for any choice of pseudo-Anosov mapping class. As a consequence one obtains a classification of the elements of the mapping class group as WeilPetersson isometries which is parallel to the Thurston classification. The second result concerns the asymptotic behavior of t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010