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Some aspects of recent works on limit theorems in ergodic theory with special emphasis on the "central limit theorem''
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Ergodic properties of signed binary expansions
An introduction to joinings in ergodic theory
| 1. | Laboratoire de Mathématiques Raphaël Salem, Université de Rouen, CNRS, Avenue de l'Université, Avenue de l'Université, 76801 Saint Étienne du Rouvray, France |
- the links between the existence of a non trivial common factor and the existence of a joining which is not the product measure,
- how joinings can be employed to provide elegant proofs of classical results,
- how joinings are involved in important questions of ergodic theory, such as pointwise convergence or Rohlin's multiple mixing problem.
| [1] |
Younghwan Son. Substitutions, tiling dynamical systems and minimal self-joinings. Discrete & Continuous Dynamical Systems, 2014, 34 (11) : 4855-4874. doi: 10.3934/dcds.2014.34.4855 |
| [2] |
Jon Chaika, Bryna Kra. A prime system with many self-joinings. Journal of Modern Dynamics, 2021, 17: 213-265. doi: 10.3934/jmd.2021007 |
| [3] |
Piotr Oprocha. Double minimality, entropy and disjointness with all minimal systems. Discrete & Continuous Dynamical Systems, 2019, 39 (1) : 263-275. doi: 10.3934/dcds.2019011 |
| [4] |
Peter W. Bates, Ji Li, Mingji Zhang. Singular fold with real noise. Discrete & Continuous Dynamical Systems - B, 2016, 21 (7) : 2091-2107. doi: 10.3934/dcdsb.2016038 |
| [5] |
Gheorghe Tigan. Degenerate with respect to parameters fold-Hopf bifurcations. Discrete & Continuous Dynamical Systems, 2017, 37 (4) : 2115-2140. doi: 10.3934/dcds.2017091 |
| [6] |
Jie Li, Kesong Yan, Xiangdong Ye. Recurrence properties and disjointness on the induced spaces. Discrete & Continuous Dynamical Systems, 2015, 35 (3) : 1059-1073. doi: 10.3934/dcds.2015.35.1059 |
| [7] |
Philipp Kunde. Smooth diffeomorphisms with homogeneous spectrum and disjointness of convolutions. Journal of Modern Dynamics, 2016, 10: 439-481. doi: 10.3934/jmd.2016.10.439 |
| [8] |
Wen Huang, Jianya Liu, Ke Wang. Möbius disjointness for skew products on a circle and a nilmanifold. Discrete & Continuous Dynamical Systems, 2021, 41 (8) : 3531-3553. doi: 10.3934/dcds.2021006 |
| [9] |
Jacek Brzykcy, Krzysztof Frączek. Disjointness of interval exchange transformations from systems of probabilistic origin. Discrete & Continuous Dynamical Systems, 2010, 27 (1) : 53-73. doi: 10.3934/dcds.2010.27.53 |
| [10] |
Karim Boulabiar, Gerard Buskes and Gleb Sirotkin. A strongly diagonal power of algebraic order bounded disjointness preserving operators. Electronic Research Announcements, 2003, 9: 94-98. |
| [11] |
Jon Chaika, Alex Eskin. Möbius disjointness for interval exchange transformations on three intervals. Journal of Modern Dynamics, 2019, 14: 55-86. doi: 10.3934/jmd.2019003 |
| [12] |
Wen Huang, Zhiren Wang, Guohua Zhang. Möbius disjointness for topological models of ergodic systems with discrete spectrum. Journal of Modern Dynamics, 2019, 14: 277-290. doi: 10.3934/jmd.2019010 |
| [13] |
Carles Bonet-Revés, Tere M-Seara. Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems. Discrete & Continuous Dynamical Systems, 2016, 36 (7) : 3545-3601. doi: 10.3934/dcds.2016.36.3545 |
| [14] |
Matúš Dirbák. Minimal skew products with hypertransitive or mixing properties. Discrete & Continuous Dynamical Systems, 2012, 32 (5) : 1657-1674. doi: 10.3934/dcds.2012.32.1657 |
| [15] |
Jean René Chazottes, F. Durand. Local rates of Poincaré recurrence for rotations and weak mixing. Discrete & Continuous Dynamical Systems, 2005, 12 (1) : 175-183. doi: 10.3934/dcds.2005.12.175 |
| [16] |
Oliver Knill. Singular continuous spectrum and quantitative rates of weak mixing. Discrete & Continuous Dynamical Systems, 1998, 4 (1) : 33-42. doi: 10.3934/dcds.1998.4.33 |
| [17] |
Ethan M. Ackelsberg. Rigidity, weak mixing, and recurrence in abelian groups. Discrete & Continuous Dynamical Systems, 2021 doi: 10.3934/dcds.2021168 |
| [18] |
Bernard Helffer, Thomas Hoffmann-Ostenhof, Susanna Terracini. Nodal minimal partitions in dimension $3$. Discrete & Continuous Dynamical Systems, 2010, 28 (2) : 617-635. doi: 10.3934/dcds.2010.28.617 |
| [19] |
Anthony Quas, Terry Soo. Weak mixing suspension flows over shifts of finite type are universal. Journal of Modern Dynamics, 2012, 6 (4) : 427-449. doi: 10.3934/jmd.2012.6.427 |
| [20] |
Corinna Ulcigrai. Weak mixing for logarithmic flows over interval exchange transformations. Journal of Modern Dynamics, 2009, 3 (1) : 35-49. doi: 10.3934/jmd.2009.3.35 |
2020 Impact Factor: 1.392
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