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Enveloping semigroups of systems of order d
1. | Centro de Modelamiento Matemático and Departamento de Ingeniería Matemática, Universidad de Chile, Av. Blanco Encalada 2120, Santiago, Chile |
References:
[1] |
J. Auslander, Minimal Flows and their Extensions, North-Holland Mathematics Studies, 153, Notas de Matemática [Mathematical Notes], 122, North-Holland Publishing Co., Amsterdam, 1988. |
[2] |
H. Becker and A. S. Kechris, The Descriptive set Theory of Polish Group Actions, London Mathematical Society Lecture Note Series, 232, Cambridge Univ. Press, Cambridge, 1996.
doi: 10.1017/CBO9780511735264. |
[3] |
R. Ellis, Lectures on Topological Dynamics, W. A. Benjamin, Inc., New York, 1969. |
[4] |
E. Glasner, Minimal nil-transformations of class two, Israel J. Math., 81 (1993), 31-51.
doi: 10.1007/BF02761296. |
[5] |
E. Glasner, Enveloping semigroups in topological dynamics, Topology Appl., 154 (2007), 2344-2363.
doi: 10.1016/j.topol.2007.03.009. |
[6] |
B. Green and T. Tao, Linear equations in primes, Ann. of Math. (2), 171 (2010), 1753-1850.
doi: 10.4007/annals.2010.171.1753. |
[7] |
B. Host and B. Kra, Nonconventional ergodic averages and nilmanifolds, Ann. of Math. (2), 161 (2005), 398-488.
doi: 10.4007/annals.2005.161.397. |
[8] |
B. Host, B. Kra and A. Maass, Nilsequences and a structure theorem for topological dynamical systems, Adv. Math., 224 (2010), 103-129.
doi: 10.1016/j.aim.2009.11.009. |
[9] |
B. Host and A. Maass, Nilsystèmes d'ordre deux et parallélépipèdes, (French) [Two step nilsystems and parallelepipeds], Bull. Soc. Math. France, 135 (2007), 367-405. |
[10] |
A. Mal'cev, On a class of homogeneous spaces, Izvestiya Akad. Nauk SSSR. Ser Mat., 13 (1949), 9-32. |
[11] |
R. Pikuła, Enveloping semigroups of unipotent affine transformations of the torus, Ergodic Theory Dynam. Systems, 30 (2010), 1543-1559.
doi: 10.1017/S0143385709000261. |
[12] |
R. J. Sacker and G. R. Sell, Finite extensions of minimal transformation groups, Trans. Amer. Math. Soc., 190 (1974), 325-334.
doi: 10.1090/S0002-9947-1974-0350715-8. |
[13] |
S. Shao and X. Ye, Regionally proximal relation of order $d$ is an equivalence one for minimal systems and a combinatorial consequence, Adv. Math., 231 (2012), 1786-1817.
doi: 10.1016/j.aim.2012.07.012. |
show all references
References:
[1] |
J. Auslander, Minimal Flows and their Extensions, North-Holland Mathematics Studies, 153, Notas de Matemática [Mathematical Notes], 122, North-Holland Publishing Co., Amsterdam, 1988. |
[2] |
H. Becker and A. S. Kechris, The Descriptive set Theory of Polish Group Actions, London Mathematical Society Lecture Note Series, 232, Cambridge Univ. Press, Cambridge, 1996.
doi: 10.1017/CBO9780511735264. |
[3] |
R. Ellis, Lectures on Topological Dynamics, W. A. Benjamin, Inc., New York, 1969. |
[4] |
E. Glasner, Minimal nil-transformations of class two, Israel J. Math., 81 (1993), 31-51.
doi: 10.1007/BF02761296. |
[5] |
E. Glasner, Enveloping semigroups in topological dynamics, Topology Appl., 154 (2007), 2344-2363.
doi: 10.1016/j.topol.2007.03.009. |
[6] |
B. Green and T. Tao, Linear equations in primes, Ann. of Math. (2), 171 (2010), 1753-1850.
doi: 10.4007/annals.2010.171.1753. |
[7] |
B. Host and B. Kra, Nonconventional ergodic averages and nilmanifolds, Ann. of Math. (2), 161 (2005), 398-488.
doi: 10.4007/annals.2005.161.397. |
[8] |
B. Host, B. Kra and A. Maass, Nilsequences and a structure theorem for topological dynamical systems, Adv. Math., 224 (2010), 103-129.
doi: 10.1016/j.aim.2009.11.009. |
[9] |
B. Host and A. Maass, Nilsystèmes d'ordre deux et parallélépipèdes, (French) [Two step nilsystems and parallelepipeds], Bull. Soc. Math. France, 135 (2007), 367-405. |
[10] |
A. Mal'cev, On a class of homogeneous spaces, Izvestiya Akad. Nauk SSSR. Ser Mat., 13 (1949), 9-32. |
[11] |
R. Pikuła, Enveloping semigroups of unipotent affine transformations of the torus, Ergodic Theory Dynam. Systems, 30 (2010), 1543-1559.
doi: 10.1017/S0143385709000261. |
[12] |
R. J. Sacker and G. R. Sell, Finite extensions of minimal transformation groups, Trans. Amer. Math. Soc., 190 (1974), 325-334.
doi: 10.1090/S0002-9947-1974-0350715-8. |
[13] |
S. Shao and X. Ye, Regionally proximal relation of order $d$ is an equivalence one for minimal systems and a combinatorial consequence, Adv. Math., 231 (2012), 1786-1817.
doi: 10.1016/j.aim.2012.07.012. |
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