Affiliation:
1. Mathematics Department , Harvard University , Cambridge , MA 02138-2901 , USA
Abstract
Abstract
This paper introduces a space of nonabelian modular symbols
𝒮
(
V
)
{{\mathcal{S}}(V)}
attached to any hyperbolic Riemann surface V,
and applies it to obtain new results on polygonal billiards and holomorphic 1-forms.
In particular, it shows the scarring behavior of periodic trajectories for billiards
in a regular polygon is governed by a countable set of measures
homeomorphic to
ω
ω
+
1
{\omega^{\omega}+1}
.
Subject
Applied Mathematics,General Mathematics
Reference37 articles.
1. B. J. Birch,
Elliptic curves over Q: A progress report,
1969 Number Theory Institute (Stony Brook 1969),
Proc. Sympos. Pure Math. 20,
American Mathematical Society, Providence (1971), 396–400.
2. D. W. Boyd and R. D. Mauldin,
The order type of the set of Pisot numbers,
Topology Appl. 69 (1996), no. 2, 115–120.
3. J. F. Brock and K. W. Bromberg,
Inflexibility, Weil–Peterson distance, and volumes of fibered 3-manifolds,
Math. Res. Lett. 23 (2016), no. 3, 649–674.
4. D. Davis and S. Lelièvre,
Periodic paths on the pentagon, double pentagon and golden L,
preprint (2018), https://arxiv.org/abs/1810.11310.
5. G. Forni,
A geometric criterion for the nonuniform hyperbolicity of the Kontsevich–Zorich cocycle. With an appendix by Carlos Matheus,
J. Mod. Dyn. 5 (2011), no. 2, 355–395.
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