`a`
Journal of Modern Dynamics (JMD)
 

The gap distribution of directions in some Schottky groups
Pages: 477 - 499, Volume 11, 2017

doi:10.3934/jmd.2017019      Abstract        References        Full text (633.1K)           Related Articles

Xin Zhang - Department of Mathematics, University of Illinois, 1409 W Green Street, Urbana, IL 61801, United States (email)

1 J. S. Athreya and J. Chaika, The distribution of gaps for saddle connection directions, Geom. Funct. Anal., 22 (2012), 1491-1516.       
2 J. S. Athreya and Y. Cheung, A Poincaré section for the horocycle flow on the space of lattices, Int. Math. Res. Not. IMRN, 10 (2014), 2643-2690.       
3 F. P. Boca, A. A. Popa and A. Zaharescu, Pair correlation of hyperbolic lattice angles, Int. J. Number Theory, 10 (2014), 1955-1989.       
4 J. Bourgain, A. Kontorovich and P. Sarnak, Sector estimates for hyperbolic isometries, Geom. Funct. Anal., 20 (2010), 1175-1200.       
5 J. Bourgain, P. Sarnak and Z. Rudnick, Local statistics of lattice points on the sphere, arXiv:1204.0134, 2012.
6 N. D. Elkies and C. T. McMullen, Gaps in $\sqrt n$ mod 1 and ergodic theory, Duke Math. J., 123 (2004), 95-139.       
7 K. J. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in Mathematics, 85, Cambridge University Press, Cambridge, 1986.       
8 A. Good, Local Analysis of Selberg's Trace Formula, Lecture Notes in Mathematics, 1040, Springer-Verlag, Berlin, 1983.       
9 D. Kelmer and A. Kontorovich, On the pair correlation density for hyperbolic angles, Duke Math. J., 164 (2015), 473-509.       
10 J. Marklof, The $n$-point correlations between values of a linear form, With an appendix by Zeév Rudnick, Ergodic Theory Dynam. Systems, 20 (2000), 1127-1172.       
11 J. Marklof and A. Strömbergsson, The distribution of free path lengths in the periodic Lorentz gas and related lattice point problems, Ann. of Math. (2), 172 (2010), 1949-2033.
12 J. Marklof and I. Vinogradov, Directions in Hyperbolic Lattices, arXiv:1409.3764, 2015.
13 C. T. McMullen, Hausdorff dimension and conformal dynamics. III. Computation of dimension, Amer. J. Math., 120 (1998), 691-721.       
14 H. Oh and N. A. Shah, Equidistribution and counting for orbits of geometrically finite hyperbolic groups, J. Amer. Math. Soc., 26 (2013), 511-562.       
15 S. J. Patterson, The limit set of a Fuchsian group, Acta Math., 136 (1976), 241-273.       
16 M. S. Risager and A. Södergren, Angles in hyperbolic lattices: The pair correlation density, Trans. Amer. Math. Soc., 369 (2017), 2807-2841.       
17 Z. Rudnick and X. Zhang, Gap distributions in circle packings, Münster J. Math., 10 (2017), 131-170.       
18 D. Sullivan, The density at infinity of a discrete group of hyperbolic motions, Inst. Hautes Études Sci. Publ. Math., 50 (1979), 171-202.       
19 D. Sullivan, Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups, Acta Math., 153 (1984), 259-277.       

Go to top