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Separated nets arising from certain higher rank $\mathbb{R}^k$ actions on homogeneous spaces
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA |
We prove that separated net arising from certain higher rank $\mathbb R.k$ actions on homogeneous spaces is bi-Lipschitz equivalent to a lattice.
References:
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D. Burago and B. Kleiner,
Separated nets in Euclidean space and Jacobians of bi-Lipschitz maps, Geom. Funct. Anal., 8 (1998), 273-282.
doi: 10.1007/s000390050056. |
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A. Haynes, M. Kelly and B. Weiss,
Equivalence relations on separated nets arising from linear toral flows, Proceedings of the London Mathematical Society, 109 (2014), 1203-1228.
doi: 10.1112/plms/pdu036. |
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A. -P. José, D. Coronel and J. -M. Gambaudo,
Linearly repetitive Delone sets are rectifiable, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 30 (2013), 275-290.
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A. Katok,
The special representation theorem for multi-dimensional group actions, Asterisque, 49 (1977), 117-140.
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C. McMullen,
Lipschitz maps and nets in Euclidean space, Geom. Funct. Anal., 8 (1998), 304-314.
doi: 10.1007/s000390050058. |
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M. Ratner,
Horocycle flows are loosely Bernoulli, Israel Journal of Mathematics, 31 (1978), 122-132.
doi: 10.1007/BF02760543. |
| [7] |
C. Salvatore and L. Flaminio,
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds, Journal of Modern Dynamics, 9 (2015), 305-353.
doi: 10.3934/jmd.2015.9.305. |
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J. Tanis, Effective equidistribution for some unipotent flows in PSL ${\left({2, \mathbb{R}} \right)^k}$ mod cocompact irreducible lattice, preprint, arXiv: 1412.5353v3 (2015). |
show all references
References:
| [1] |
D. Burago and B. Kleiner,
Separated nets in Euclidean space and Jacobians of bi-Lipschitz maps, Geom. Funct. Anal., 8 (1998), 273-282.
doi: 10.1007/s000390050056. |
| [2] |
A. Haynes, M. Kelly and B. Weiss,
Equivalence relations on separated nets arising from linear toral flows, Proceedings of the London Mathematical Society, 109 (2014), 1203-1228.
doi: 10.1112/plms/pdu036. |
| [3] |
A. -P. José, D. Coronel and J. -M. Gambaudo,
Linearly repetitive Delone sets are rectifiable, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 30 (2013), 275-290.
doi: 10.1016/j.anihpc.2012.07.006. |
| [4] |
A. Katok,
The special representation theorem for multi-dimensional group actions, Asterisque, 49 (1977), 117-140.
|
| [5] |
C. McMullen,
Lipschitz maps and nets in Euclidean space, Geom. Funct. Anal., 8 (1998), 304-314.
doi: 10.1007/s000390050058. |
| [6] |
M. Ratner,
Horocycle flows are loosely Bernoulli, Israel Journal of Mathematics, 31 (1978), 122-132.
doi: 10.1007/BF02760543. |
| [7] |
C. Salvatore and L. Flaminio,
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds, Journal of Modern Dynamics, 9 (2015), 305-353.
doi: 10.3934/jmd.2015.9.305. |
| [8] |
J. Tanis, Effective equidistribution for some unipotent flows in PSL ${\left({2, \mathbb{R}} \right)^k}$ mod cocompact irreducible lattice, preprint, arXiv: 1412.5353v3 (2015). |
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