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Fluctuations of ergodic sums for horocycle flows on $\Z^d$covers of finite volume surfaces
1.  Department of Mathematics, 255 Hurley Hall, University of Notre Dame, Notre Dame IN 465564618, United States 
2.  Department of Mathematics, The Pennsylvania State University, University Park, PA 16802 
[1] 
Andreas Strömbergsson. On the deviation of ergodic averages for horocycle flows. Journal of Modern Dynamics, 2013, 7 (2) : 291328. doi: 10.3934/jmd.2013.7.291 
[2] 
François Ledrappier, Omri Sarig. Unique ergodicity for nonuniquely ergodic horocycle flows. Discrete & Continuous Dynamical Systems  A, 2006, 16 (2) : 411433. doi: 10.3934/dcds.2006.16.411 
[3] 
Francois Ledrappier and Omri Sarig. Invariant measures for the horocycle flow on periodic hyperbolic surfaces. Electronic Research Announcements, 2005, 11: 8994. 
[4] 
Tanja Eisner, Jakub Konieczny. Automatic sequences as good weights for ergodic theorems. Discrete & Continuous Dynamical Systems  A, 2018, 38 (8) : 40874115. doi: 10.3934/dcds.2018178 
[5] 
Mrinal Kanti Roychowdhury. Quantization coefficients for ergodic measures on infinite symbolic space. Discrete & Continuous Dynamical Systems  A, 2014, 34 (7) : 28292846. doi: 10.3934/dcds.2014.34.2829 
[6] 
Kathryn Lindsey, Rodrigo Treviño. Infinite type flat surface models of ergodic systems. Discrete & Continuous Dynamical Systems  A, 2016, 36 (10) : 55095553. doi: 10.3934/dcds.2016043 
[7] 
Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Minimality of the horocycle flow on laminations by hyperbolic surfaces with nontrivial topology. Discrete & Continuous Dynamical Systems  A, 2016, 36 (9) : 46194635. doi: 10.3934/dcds.2016001 
[8] 
Yuri Kifer. Ergodic theorems for nonconventional arrays and an extension of the Szemerédi theorem. Discrete & Continuous Dynamical Systems  A, 2018, 38 (6) : 26872716. doi: 10.3934/dcds.2018113 
[9] 
Zuohuan Zheng, Jing Xia, Zhiming Zheng. Necessary and sufficient conditions for semiuniform ergodic theorems and their applications. Discrete & Continuous Dynamical Systems  A, 2006, 14 (3) : 409417. doi: 10.3934/dcds.2006.14.409 
[10] 
Julia Brettschneider. On uniform convergence in ergodic theorems for a class of skew product transformations. Discrete & Continuous Dynamical Systems  A, 2011, 29 (3) : 873891. doi: 10.3934/dcds.2011.29.873 
[11] 
David Ralston, Serge Troubetzkoy. Ergodic infinite group extensions of geodesic flows on translation surfaces. Journal of Modern Dynamics, 2012, 6 (4) : 477497. doi: 10.3934/jmd.2012.6.477 
[12] 
Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky. Corrigendum to "Minimality of the horocycle flow on laminations by hyperbolic surfaces with nontrivial topology". Discrete & Continuous Dynamical Systems  A, 2017, 37 (8) : 45854586. doi: 10.3934/dcds.2017196 
[13] 
Vladimir S. Matveev and Petar J. Topalov. Metric with ergodic geodesic flow is completely determined by unparameterized geodesics. Electronic Research Announcements, 2000, 6: 98104. 
[14] 
Yves Derriennic. Some aspects of recent works on limit theorems in ergodic theory with special emphasis on the "central limit theorem''. Discrete & Continuous Dynamical Systems  A, 2006, 15 (1) : 143158. doi: 10.3934/dcds.2006.15.143 
[15] 
Osama Khalil. Geodesic planes in geometrically finite manifolds. Discrete & Continuous Dynamical Systems  A, 2019, 39 (2) : 881903. doi: 10.3934/dcds.2019037 
[16] 
Ya Wang, Fuke Wu, Xuerong Mao, Enwen Zhu. Advances in the LaSalletype theorems for stochastic functional differential equations with infinite delay. Discrete & Continuous Dynamical Systems  B, 2020, 25 (1) : 287300. doi: 10.3934/dcdsb.2019182 
[17] 
K. A. Ariyawansa, Leonid Berlyand, Alexander Panchenko. A network model of geometrically constrained deformations of granular materials. Networks & Heterogeneous Media, 2008, 3 (1) : 125148. doi: 10.3934/nhm.2008.3.125 
[18] 
Giovanni Forni, Corinna Ulcigrai. Timechanges of horocycle flows. Journal of Modern Dynamics, 2012, 6 (2) : 251273. doi: 10.3934/jmd.2012.6.251 
[19] 
Oliver Jenkinson. Ergodic Optimization. Discrete & Continuous Dynamical Systems  A, 2006, 15 (1) : 197224. doi: 10.3934/dcds.2006.15.197 
[20] 
Azhar Ali Zafar, Khurram Shabbir, Asim Naseem, Muhammad Waqas Ashraf. MHD natural convection boundarylayer flow over a semiinfinite heated plate with arbitrary inclination. Discrete & Continuous Dynamical Systems  S, 2020, 13 (3) : 10071015. doi: 10.3934/dcdss.2020059 
2018 Impact Factor: 1.143
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