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Universal skyscraper templates for infinite measure preserving transformations
Tiling Abelian groups with a single tile
1.  Northeastern University, Department of Mathematics, Boston, MA 02115 
2.  University of Massachusetts Lowell, Department of Mathematics, One University Avenue, Lowell, MA 01854, United States 
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Mrinal Kanti Roychowdhury. Quantization coefficients for ergodic measures on infinite symbolic space. Discrete & Continuous Dynamical Systems, 2014, 34 (7) : 28292846. doi: 10.3934/dcds.2014.34.2829 
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Kathryn Lindsey, Rodrigo Treviño. Infinite type flat surface models of ergodic systems. Discrete & Continuous Dynamical Systems, 2016, 36 (10) : 55095553. doi: 10.3934/dcds.2016043 
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A. Pedas, G. Vainikko. Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Communications on Pure & Applied Analysis, 2006, 5 (2) : 395413. doi: 10.3934/cpaa.2006.5.395 
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Jon Chaika, Howard Masur. There exists an interval exchange with a nonergodic generic measure. Journal of Modern Dynamics, 2015, 9: 289304. doi: 10.3934/jmd.2015.9.289 
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Jialu Fang, Yongluo Cao, Yun Zhao. Measure theoretic pressure and dimension formula for nonergodic measures. Discrete & Continuous Dynamical Systems, 2020, 40 (5) : 27672789. doi: 10.3934/dcds.2020149 
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Nuno Luzia. On the uniqueness of an ergodic measure of full dimension for nonconformal repellers. Discrete & Continuous Dynamical Systems, 2017, 37 (11) : 57635780. doi: 10.3934/dcds.2017250 
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Tomasz Downarowicz, Benjamin Weiss. Pure strictly uniform models of nonergodic measure automorphisms. Discrete & Continuous Dynamical Systems, 2022, 42 (2) : 863884. doi: 10.3934/dcds.2021140 
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Charlene Kalle, Niels Langeveld, Marta Maggioni, Sara Munday. Matching for a family of infinite measure continued fraction transformations. Discrete & Continuous Dynamical Systems, 2020, 40 (11) : 63096330. doi: 10.3934/dcds.2020281 
[10] 
Roland Zweimüller. Asymptotic orbit complexity of infinite measure preserving transformations. Discrete & Continuous Dynamical Systems, 2006, 15 (1) : 353366. doi: 10.3934/dcds.2006.15.353 
[11] 
S. Eigen, A. B. Hajian, V. S. Prasad. Universal skyscraper templates for infinite measure preserving transformations. Discrete & Continuous Dynamical Systems, 2006, 16 (2) : 343360. doi: 10.3934/dcds.2006.16.343 
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Roland Gunesch, Anatole Katok. Construction of weakly mixing diffeomorphisms preserving measurable Riemannian metric and smooth measure. Discrete & Continuous Dynamical Systems, 2000, 6 (1) : 6188. doi: 10.3934/dcds.2000.6.61 
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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 
[14] 
Yanfeng Qi, Chunming Tang, Zhengchun Zhou, Cuiling Fan. Several infinite families of pary weakly regular bent functions. Advances in Mathematics of Communications, 2018, 12 (2) : 303315. doi: 10.3934/amc.2018019 
[15] 
Nasab Yassine. Quantitative recurrence of some dynamical systems preserving an infinite measure in dimension one. Discrete & Continuous Dynamical Systems, 2018, 38 (1) : 343361. doi: 10.3934/dcds.2018017 
[16] 
Guizhen Cui, Yan Gao. Wandering continua for rational maps. Discrete & Continuous Dynamical Systems, 2016, 36 (3) : 13211329. doi: 10.3934/dcds.2016.36.1321 
[17] 
Guizhen Cui, Wenjuan Peng, Lei Tan. On the topology of wandering Julia components. Discrete & Continuous Dynamical Systems, 2011, 29 (3) : 929952. doi: 10.3934/dcds.2011.29.929 
[18] 
Scott Schmieding, Rodrigo Treviño. Random substitution tilings and deviation phenomena. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 38693902. doi: 10.3934/dcds.2021020 
[19] 
Eli Glasner, Benjamin Weiss. A generic distal tower of arbitrary countable height over an arbitrary infinite ergodic system. Journal of Modern Dynamics, 2021, 17: 435463. doi: 10.3934/jmd.2021015 
[20] 
Ian Melbourne, Dalia Terhesiu. Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure. Journal of Modern Dynamics, 2018, 12: 285313. doi: 10.3934/jmd.2018011 
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