-
Previous Article
On nonlocal symmetries generated by recursion operators: Second-order evolution equations
- DCDS Home
- This Issue
-
Next Article
Positive ground state solutions for a quasilinear elliptic equation with critical exponent
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:
[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). |
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). |
[1] |
Salvatore Cosentino, Livio Flaminio. Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds. Journal of Modern Dynamics, 2015, 9: 305-353. doi: 10.3934/jmd.2015.9.305 |
[2] |
J. Douglas Wright. On the spectrum of the superposition of separated potentials.. Discrete and Continuous Dynamical Systems - B, 2013, 18 (1) : 273-281. doi: 10.3934/dcdsb.2013.18.273 |
[3] |
Benjamin Dozier. Equidistribution of saddle connections on translation surfaces. Journal of Modern Dynamics, 2019, 14: 87-120. doi: 10.3934/jmd.2019004 |
[4] |
Stefano Cosenza, Paolo Crucitti, Luigi Fortuna, Mattia Frasca, Manuela La Rosa, Cecilia Stagni, Lisa Usai. From Net Topology to Synchronization in HR Neuron Grids. Mathematical Biosciences & Engineering, 2005, 2 (1) : 53-77. doi: 10.3934/mbe.2005.2.53 |
[5] |
Brandon Seward. Every action of a nonamenable group is the factor of a small action. Journal of Modern Dynamics, 2014, 8 (2) : 251-270. doi: 10.3934/jmd.2014.8.251 |
[6] |
Michael Hutchings. Mean action and the Calabi invariant. Journal of Modern Dynamics, 2016, 10: 511-539. doi: 10.3934/jmd.2016.10.511 |
[7] |
David Bechara Senior, Umberto L. Hryniewicz, Pedro A. S. Salomão. On the relation between action and linking. Journal of Modern Dynamics, 2021, 17: 319-336. doi: 10.3934/jmd.2021011 |
[8] |
Wenyu Pan. Effective equidistribution of circles in the limit sets of Kleinian groups. Journal of Modern Dynamics, 2017, 11: 189-217. doi: 10.3934/jmd.2017009 |
[9] |
Runlin Zhang. Equidistribution of translates of a homogeneous measure on the Borel–Serre compactification. Discrete and Continuous Dynamical Systems, 2022, 42 (4) : 2053-2071. doi: 10.3934/dcds.2021183 |
[10] |
V. Kumar Murty, Ying Zong. Splitting of abelian varieties. Advances in Mathematics of Communications, 2014, 8 (4) : 511-519. doi: 10.3934/amc.2014.8.511 |
[11] |
John Franks, Michael Handel, Kamlesh Parwani. Fixed points of Abelian actions. Journal of Modern Dynamics, 2007, 1 (3) : 443-464. doi: 10.3934/jmd.2007.1.443 |
[12] |
Helmut Kröger. From quantum action to quantum chaos. Conference Publications, 2003, 2003 (Special) : 492-500. doi: 10.3934/proc.2003.2003.492 |
[13] |
Carlos Munuera, Wanderson Tenório, Fernando Torres. Locally recoverable codes from algebraic curves with separated variables. Advances in Mathematics of Communications, 2020, 14 (2) : 265-278. doi: 10.3934/amc.2020019 |
[14] |
Chady Ghnatios, Guangtao Xu, Adrien Leygue, Michel Visonneau, Francisco Chinesta, Alain Cimetiere. On the space separated representation when addressing the solution of PDE in complex domains. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 475-500. doi: 10.3934/dcdss.2016008 |
[15] |
Sandra Carillo, Mauro Lo Schiavo, Cornelia Schiebold. Abelian versus non-Abelian Bäcklund charts: Some remarks. Evolution Equations and Control Theory, 2019, 8 (1) : 43-55. doi: 10.3934/eect.2019003 |
[16] |
Magdalena Czubak, Robert L. Jerrard. Topological defects in the abelian Higgs model. Discrete and Continuous Dynamical Systems, 2015, 35 (5) : 1933-1968. doi: 10.3934/dcds.2015.35.1933 |
[17] |
Eldho K. Thomas, Nadya Markin, Frédérique Oggier. On Abelian group representability of finite groups. Advances in Mathematics of Communications, 2014, 8 (2) : 139-152. doi: 10.3934/amc.2014.8.139 |
[18] |
S. Eigen, V. S. Prasad. Tiling Abelian groups with a single tile. Discrete and Continuous Dynamical Systems, 2006, 16 (2) : 361-365. doi: 10.3934/dcds.2006.16.361 |
[19] |
Sanghoon Kwon, Seonhee Lim. Equidistribution with an error rate and Diophantine approximation over a local field of positive characteristic. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 169-186. doi: 10.3934/dcds.2018008 |
[20] |
Nimish Shah, Lei Yang. Equidistribution of curves in homogeneous spaces and Dirichlet's approximation theorem for matrices. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5247-5287. doi: 10.3934/dcds.2020227 |
2021 Impact Factor: 1.588
Tools
Metrics
Other articles
by authors
[Back to Top]