We present a theory of self-joinings for semisimple maps and their group extensions which is a unification of the following three cases studied so far: (iii) Gaussian-Kronecker automorphisms: [Th], [Ju-Th]. (ii) MSJ and simple automorphisms: [Ru], [Ve], [Ju-Ru]. (iii) Group extension of discrete spectrum automorphisms: [Le-Me], [Le], [Me].
@article{bwmeta1.element.bwnjournal-article-smv112i2p141bwm,
author = {A. Del Junco and M. Lema\'nczyk and M. Mentzen},
title = {Semisimplicity, joinings and group extensions},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {141-164},
zbl = {0814.28007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv112i2p141bwm}
}
Del Junco, A.; Lemańczyk, M.; Mentzen, M. Semisimplicity, joinings and group extensions. Studia Mathematica, Tome 113 (1995) pp. 141-164. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv112i2p141bwm/
[00000] [An] H. Anzai, Ergodic skew product transformations on the torus, Osaka J. Math. 3 (1951), 83-99. | Zbl 0043.11203
[00001] [Fi-Ru] A. Fieldsteel and D. Rudolph, An ergodic transformation with trivial Kakutani centralizer, Ergodic Theory Dynamical Systems 12 (1992), 459-478. | Zbl 0763.58016
[00002] [Fu] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton University Press, Princeton, N.J., 1981. | Zbl 0459.28023
[00003] [Gl-Ho-Ru] E. Glasner, B. Host and D. Rudolph, Simple systems and their higher order self-joinings, Israel J. Math. 78 (1992), 131-142. | Zbl 0779.28010
[00004] [Ju-Ru] A. del Junco and D. Rudolph, On ergodic actions whose self-joinings are graphs, Ergodic Theory Dynamical Systems 7 (1987), 531-557. | Zbl 0646.60010
[00005] [Ju-Th] A. del Junco and J.-P. Thouvenot, The theory for Gaussian-Kronecker automorphisms, preprint.
[00006] [Ke-Ne1] H. B. Keynes and D. Newton, Choquet Theory and Ergodic Measures for Compact Group Extensions, Lecture Notes in Math. 318, Springer, 1973. | Zbl 0256.28014
[00007] [Ke-Ne2] H. B. Keynes and D. Newton, The structure of ergodic measures for compact group extensions, Israel J. Math. 18 (1974), 363-389. | Zbl 0299.54033
[00008] [Ke-Ne3] H. B. Keynes and D. Newton, Ergodic measures for nonabelian compact group extensions, Compositio Math. 32 (1976), 53-70. | Zbl 0318.28006
[00009] [Le] M. Lemańczyk, Ergodic abelian group extensions of rotations, preprint, Toruń 1990.
[00010] [Le] M. Lemańczyk and M. K. Mentzen, Compact subgroups in the centralizer of natural factors of an ergodic group extension of a rotation determine all factors, Ergodic Theory Dynamical Systems 10 (1990), 763-776. | Zbl 0725.54030
[00011] [Me] M. K. Mentzen, Ergodic properties of group extensions of dynamical systems with discrete spectra, Studia Math. 101 (1991), 19-31. | Zbl 0809.28015
[00012] [Ne] D. Newton, On canonical factors of ergodic dynamical systems, J. London Math. Soc. 19 (1979), 129-136. | Zbl 0425.28012
[00013] [Ne1] D. Newton, Coalescence and spectrum of automorphisms of a Lebesgue space, Z. Wahrsch. Verw. Gebiete 19 (1971), 117-122. | Zbl 0201.38401
[00014] [Ru] D. Rudolph, An example of measure preserving map with minimal self-joinings, and applications, J. Analyse Math. 35 (1979), 97-122. | Zbl 0446.28018
[00015] [Ru1] D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, ibid. 34 (1978), 36-60. | Zbl 0415.28012
[00016] [Th] J.-P. Thouvenot, The metrical structure of some Gaussian processes, in: Proc. Ergodic Theory and Related Topics II, Georgenthal 1986, 195-198.
[00017] [Ve] W. A. Veech, A criterion for a process to be prime, Monatsh. Math. 94 (1982), 335-341. | Zbl 0499.28016
[00018] [Zi] R. Zimmer, Extensions of ergodic group actions, Illinois J. Math. 20 (1976), 373-409. | Zbl 0334.28015
[00019] [Zi1] R. Zimmer, Ergodic actions with generalized discrete spectrum, ibid., 555-588. | Zbl 0349.28011