Geodesic
Minimal systems and distributionally scrambled sets
[Systèmes minimaux et ensembles distributionnellement brouillés]
Bulletin de la Société Mathématique de France, Tome 140 (2012) no. 3, pp. 401-439
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In this paper we investigate numerous constructions of minimal systems from the point of view of (ℱ 1 ,ℱ 2 )-chaos (but most of our results concern the particular cases of distributional chaos of type 1 and 2). We consider standard classes of systems, such as Toeplitz flows, Grillenberger K-systems or Blanchard-Kwiatkowski extensions of the Chacón flow, proving that all of them are DC2. An example of DC1 minimal system with positive topological entropy is also introduced. The above mentioned results answer a few open problems known from the literature.

DOI : 10.24033/bsmf.2631
Classification : 37B05, 37B40, 37B10
Keywords: chaotic pair, scrambled set, Mycielski set, distributional chaos, Li-Yorke chaos, filter
Mots-clés : paire chaotique, ensemble ***, ensemble de Mycielski, chaos distributionnel, chaos de Li-Yorke, filtre 
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     title = {Minimal systems and distributionally scrambled sets},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {401--439},
     year = {2012},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {140},
     number = {3},
     doi = {10.24033/bsmf.2631},
     zbl = {1278.37013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.24033/bsmf.2631/}
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Oprocha, Piotr. Minimal systems and distributionally scrambled sets. Bulletin de la Société Mathématique de France, Tome 140 (2012) no. 3, pp. 401-439. doi: 10.24033/bsmf.2631

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